Callbacks and Callforwards

Final Fantasy has alway been a series that has carries over recurring elements or themes. For Final Fantasy III, a number of its aspects have been referenced or carried over to later games. It is unlikely that this will be a full list, but here's some examples of how later games reference III:

Final Fantasy

A retroactive example: The Earthgift Shrine of the Souls of Chaos campaign in the Dawn of Souls and 20th Anniversary editions uses the Dark Crystal bosses from Final Fantasy III. In the latter, a remix of Final Fantasy III's Battle 2 also plays.

Final Fantasy IV

Final Fantasy IV was born out of a desire to expand upon the jobs of Final Fantasy III. Thus, each party member is modeled after a specific job, a number of which originated from III such as Bard and Sage.

Final Fantasy IV uses the concept of Dark Crystals as well as a "reverse world" as in III, although in IV's case, it's more literal.

The Final Fantasy IV Document Settings book mentions that the first king of Damcyan, the kingdom that Edward the bard is prince of, is named Duster, named after the town of bards in Final Fantasy III.

Final Fantasy VIII

One of the major backstory elements of FFVIII is Hyne the Magician, otherwise known as "Great Hyne". There are several versions of the legend cited throughout VIII (2 in-game, one as a short story from the original Ultimania), but all are roughly the same:
Hyne was a god who fought numerous beasts. Eventually, Hyne grew tired and created hyper-capable tools to do work for him while he slept. Said tools are humans. When Hyne awoke, many things were different, but most pressing were the amount of humans. Hyne decided to cull their numbers by using magic to set the "smaller humans" (i.e. children) on fire and burn them up. The other humans were understandably pissed and a war broke out between them and Hyne.
With the war turning in favor of the humans, Hyne offered up half of his body in exchange for peace. Inevitably, the magical potential in Hyne's body led the humans to war amongst each other, and by the time it was over, a sage revealed that Hyne had not given them his body, but rather his skin which was useless. Hyne himself had vanished and humanity looked for him for centuries, although it is theorized that Hein's power was passed on to the sorceresses.
Hyne targetting children is likely a reference to FFIII's protagonists while Hyne tricking humanity by giving them his skin is based on his skeletal appearance.

Final Fantasy XIV

The Syrcus Tower raid is one long extended adaptation of FFIII's endgame, with the plot tweaked to fit within the world of Eorzea. All of the monsters, mini-bosses and bosses are based on III, the major characters are Doga, Unei, Amon (who takes heavy cues from Hein) and Xande; reimagined as an Emperor who, upon being brought back from the dead, becomes nihilistic, and the final boss of the raid is The Cloud of Darkness, reimagined as a Voidsent. While not making physical appearances, Desch and Salina are also alluded to in the lore, with G'raha Tia (a notable character of the raid who eventually becomes a major character) being inspired by and connected to Desch. At the end of the Raid series, G'raha seals himself within the Tower, a nod to Desch being sealed within the Tower of Owen and sacrificing himself in the Tower's boiler room.

The concept of a group known as the Warriors of Darkness is used in Final Fantasy XIV's plotline. Their main party uses jobs available in III: Warrior, Knight, Ranger, Magus and Devout. The Knight is something of a multi-lingual reference: In english territories more familiar with the remake, it will match the Knight job as it is portrayed there. In Japan, however the job instead uses the terminology for Dark Knight (usually translated in english as Warmage), making it a nod to the job's Famicom incarnation. In what may or may not be a coincidence, Three of the used jobs closely match those the remake characters are associated with (Warrior, Devout = White Mage, Magus = Black Mage) with only the Ranger and the (Dark) Knight as outliers (though it should be noted that the WoDs appearance predates Red Mage being added to the game).

One of the available minions is modeled after the original Onion Knight from Final Fantasy III. A nod to the remake is also in the Japanese description, where it notes the name "Luneth" on the sole of the minion, although it's left ambiguous as to what the name means.

The Shadowbringers expansion takes heavy cues from III, focusing on a Flood of Light and entering the home world of the Warriors of Darkness. Additionally, Amano's more human design for the Cloud of Darkness also appears as a boss. On a more coincidental note, the character Taynor, brother of the WoDs' magus and who becomes a Black Mage himself, bears a resemblence to Arc and is even time-displaced in a similar manner that the FF3 remake protagonists were. However, it is unclear if this is an intentional reference or purely a coincidence.
The Forbidden Land, Eureka gets its name from a combination of the area of the same name (Eureka) and the music theme for said area (The Forbidden Land) from Final Fantasy III. The purpose of the area is also to get powerful weapons, much like how Eureka in III played host to some of the game's strongest weapons.

Eureka Orthos, a Deep Dungeon introduced in Endwalker, is also based on the Eureka of Final Fantasy III. It is a laboratory underneath the Crystal Tower, unlike the previous Eureka and much like how the Eureka in III was accessed via the Crystal Tower's first floor. One of the mechanics of the dungeon involves the ability to summon 'demi-clones' of XIV's Doga, Unei and an Onion Knight, calling back to the clones of Doga and Unei from III (which themselves were already referenced in the Syrcus Tower raid).

In a likely coincidental turn, the backstory for the War of the Magi in XIV involves two nations who are at war. One nation refines magic into Black Magic, but some of the mages revolt to the other side, resulting in the creation of White Magic. While the finer details vary heavily, old strategy guides for the original FFIII used a similar idea for its explanation of magic.

Ivalice: Final Fantasy Tactics + Final Fantasy XII

Final Fantasy Tactics has "Wonders" which reference prior (up to that point) games. Final Fantasy III has a slew of references through the Wonders, namely Tozus, Falgabard, the Crystal Tower (and the Ancients' Maze, by extension) and Eureka. Most of these have different backgrounds, fitting into the world of Final Fantasy Tactics (specifically, prior to an event known as the Cataclysm), though some such as Falgabard still retain references to their game of origin.

Final Fantasy Tactics also has "artifacts", items that are similar to Wonders. In addition to the Gnomish Bread being an artifact, the four magicite pieces are credited to Saronia.

The War of the Lions release included two new jobs: The Onion Knight job and the Dark Knight job. both are similar in design to the Final Fantasy III remake' job design. Given that the remake released in 2006 and War of the Lions in 2007, this is probably due to Yoshida working on both games back to back or at the same time.
In an interview, Yoshida confirmed that the Onion Knight job was more or less taken from IIIDS, but says that the Dark Knight job was primarily inspired by Cecil Harvey, although he adds that there were a lot of other things added.

In the data for both versions of the game exists a command known as "Phantom" that claims to be for a "Hell Magician"(PS1)/"Nether Shaman"(WoTL) job. In Japanese, these jobs are known as "魔界幻士", which is also the term used by the Evoker job in Final Fantasy III. It is generally thought to be the job for Elidibus, a secret boss who briefly appears in human form before transforming into a Lucavi/demon. This speculation is strengthened when a similar references appears in Final Fantasy XII, with the job now translated as "Summoner".

Stranger Of Paradise: Final Fantasy Origin

One of the levels in Stranger of Paradise is the Crystal Mirage, a 'prototype' for the Mirage Tower. As with all of the other locations in Stranger of Paradise, it is modeled after an area from another game, in this case the Crystal Tower from Final Fantasy III. Likewise, the Fool's Missive for the area notes that it is based on a location from "Dimension 3".

In the "Trials of the Dragon King" DLC, 'Evoker' and 'Ultima' subjobs can be unlocked for Jack. The Sage's Ultima subjob has the "Soul of Xande" ability.

Final Fantasy Dimensions

The game's entire premise is based around the concept of the Warriors of Light and the Warriors of Darkness from Final Fantasy III, along with having a World of Light and a World of Darkness. Unlike in III, however, the two worlds begin as one and are split when the crystal shatters in the early chapters, mixing the concept up with Final Fantasy V.

Falgabard is reinterpreted as Castle Falgabard, which is placed in the World of Darkness. It is a home for Dark Knights and nestled in the mountains, although by the time the Warriors of Darkness pass through, the castle has been bombed by the Empire, killing practically everyone. Interestingly, Nacht - the serious member of the Warriors of Darkness - hails from Falgabard, echoing Ingus from the remake, who is heavily implied to be from the covert village. While Matrix Software worked on both Dimensions and the III remake, there doesn't seem to be much staff overlap, making it questionable how intentional this was.

Dissidia Final Fantasy

Original Duology + NT

Onion Knight and the Cloud of Darkness appear as the representatives of Final Fantasy III. Much dialogue both towards and from them references the game. This includes match intro/outro quotes as well as some of the voice clips in NT.

Dissidia features the World of Darkness, based on the Cloud of Darkness' chamber. The Omega version of the stage randomly shifts to cramped, smaller arenas, referencing the dungeon itself.

The tutorials discussing play plans are narrated by a Warrior, a Black Mage, a White Mage and a Red Mage: The subtle details in the sprites show that these are intended to be the FFIII iterations of these jobs instead of FFI. Coincidentally (?) the order and classes of these four match the characters from the 3D remake.

The Onion Knight's first costume is named "Luneth" and changes his facial features and hair to resemble the character from the remake. The actual armor resembles the Warrior from Amano's artwork for the game. Onion Knight's second costume (introduced in Duodecim) is more closely based on the figure frm a specific art piece that gives him a black color scheme. In NT, the second costume returns and the color swaps reference both colors.

Onion Knight's DLC costume in 012 is based on the jobs' appearances in the 3D remake. Specifically, it gives Onion Knight Ingus' Onion Knight, Ninja and Sage job outfits (Ninja featuring Ingus' pendant and Sage containing traces of Ingus' freelancer outfit). While the western version of the DLC is named after the character it is based on, the Japanese version is named "Deformation-Style", a nod to the original platform that the game was released for.

The Cloud of Darkness' costumes are a nod to its arrival whenever the forces of light or dark grow unbalanced. In NT, the "Lucent Robe" costume returns and is made more unique.

The Cloud of Darkness' EX form is based on its form in-game. NT would eventually get an outfit based on its appearance as well.

The Crystal Tower appears as a stage in Duodecim, with the Ancient's Maze surrounding the area. One of the battlegen items from this stage is "Xande's Hatred".

The Floating Continent appears as a stage in NT, taking cues from the original field sprite as well as the CG opening for the 3D remake. The stage's description also alludes to its portrayal in the 3D remake, stating that it had been cutoff from the mainland for so long as to have its own divergent history.

Opera Omnia

Xande and Desch appear as party members. Xande's moveset is based on the original famicom game while Desch's takes inspiration from the 3D remake.

Act 3 Chapter 1 takes place in the Tower of Owen while the finale of Act 3 takes place in the World of Darkness. A chapter in Act 4 takes place in the Crystal Tower[1]. The design of the World of Darkness this time is based heavily on the 3D remake while the design for the Crystal Tower more closely resembles its map sprite.

The overarching antagonist of Act 3 is the Cloud of Darkness, who senses that the balance is tipping towards light and seeks to 'correct' it. The finale of Act 3 reenacts the ending of Final Fantasy III, complete with a "fight" against the Cloud of Darkness that is unwinnable. The Cloud of Darkness itself takes the form it took during the final battle, continuing the trend the game had of villains accessing their final boss forms.

Bravely Default

The Bravely Default series has the same producer as the Final Fantasy III remake, so nods to that game crop up every so often. One example is with summons: A buff-focused version of the Evoker appears in the form of the Conjurer job and a proper Summoner job also appears. Another is Bravely Default 2's "Hellblade" job whose Japanese name is the same as III's rendition of Dark Knight.

Tiz Arrior in Bravely Default and Yew Genologia in Bravely Second: End Layer have the Onion Shirt (BD)/Onion Knight Garb (BS) as costumes. The outfit is based on the Final Fantasy III remake's rendition of the outfit (most specifically Ingus' due to it being red).

The Water Crystal chapter of Bravely Default contains numerous references to Final Fantasy III, such as featuring a Land Turtle as a boss and the Water Crystal being sealed to prevent darkness from overtaking it. The vestals can also be considered an expansion of the concept of the Water Maidens, up to their duty to protect the crystals and their ability to revive them.

As the precurser to Bravely, A few nods are also scattered throughout Final Fantasy: The 4 Heroes of Light, such as the Dark Fencer job's japanese name being repurposed from an unused name for 3R's rendition of Dark Knight (with an armor, localized as the "Warmage Armor" having similar design to III's Dark Knight).

[1]: The Tower of Owen and the Crystal Tower are represented largely on the map screen: the actual battle environments reuse prior locations, namely the Ronka Ruins from Act 2 and the Crystal Room from the Act 1 interlude.

Final Fantasy III Beyond Final Fantasy III