Retconjuration

Black Mage: How do you keep doing that?
Sarda: It's a simple Re-Write Reality According To Your Whim spell.

—8-Bit Theater, "Episode 1131: Turnabout Isn't Fair Play"

If a Retcon is changing the past, and a Cosmic Retcon is an in-universe changing of the past, then Retconjuration ~~never happened~~ is the ability to create a Cosmic Retcon. Possibly a subtrope of Reality Warper, and ~~was once mayor of New York~~ may or may not involve leaning on, painting or breaking the Fourth Wall, or pressing a literal Reset Button. (Although, depending on the scale of the Retconjuration instance, it may categorically force other in-universe examples of Reality Warper into becoming an in-universe subtrope of Retconjuration itself.)

There are two flavors of this trope, items that allow individuals to change the past (a Time Machine being the Trope Codifier) and individuals who can change the past under their own power. Said individuals may believe themselves to be deities, and depending on the scope of the power, they ~~can't resist the taste of Trope Co Delicious Fruit Pies~~ might not be wrong.

Compare Peggy Sue. Contrast Ret-Gone.

Examples of Retconjuration include:

Anime and Manga

Madoka using her wish to do this in the final episode of Puella Magi Madoka Magica.
Doing this is Tsukishima's entire schtick in Bleach. He doesn't actually warp reality - he just inserts himself into the target's memories up to the point where they think he's always been in their lives. Creepy. What makes this even worse is that he can apply similar changes to himself, allowing him to retroactively memorize opponents' battle strategies, for example.
In Another, a class is plagued by a curse kills members of the class and immediate family. This is caused by the presence of an extra, Dead All Along, student. Retconjuration comes into play because it's impossible to identify the "Extra" due to all the students having False Memories of that presence. On top of that, even official paperwork has incorrect information. Identifying the "Extra" can only be done after the school year ends, because everything reverts back to normal at that point.
- Transformers Cybertron: In Japan, it wasn't connected to Transformers Armada and Transformers Energon. In America it was, and any inconsistencies were explained in a comic book as being the black hole that was the main problem in TFC spreading its effects across reality, causing events to not always match up. This makes it the possible reason for every plot hole in any Transformers work.

Comic Books

Superboy Prime does this by punching.
Spider-Man, Mephisto, "One More Day"

Film

Nero does this by accident in the latest Star Trek film, attacking the Kelvin and setting Starfleet down on a rather more militaristic bent. Also Vulcan is gone.
- He created an alternate reality, not a retcon... well, not entirely. It was used to restart the entire Star Trek line of movies over from scratch without actually tampering with established lore from the previous movies or series.
In the mostly horrible Nicholas Cage film Next, the lead character has a limited version of this ability, which he uses to stop terrorists and score dates with younger women.

Literature

The Wheel of Time's Balefire is a handy, portable way to do this, essentially burning the affected individual's "thread" out of existence. Not everybody's happy about this happening.
- Also, there's a Ter'angreal that does it. Uncontrollably. Only the most depraved villains are willing to even go near the thing.
Ursula K. Le Guin's The Lathe of Heaven: George Orr's "effective dreams" change not only the present but the past as well: people don't realize that the world has changed (and was different in the past).
Discworld yeti can leave a "bookmark" at some moment in time and later snap back to it if they are killed or in other troubles -- now knowing what's going to happen and able to avoid it. They died out. Several times.
- Or, for those who aren't aware of the entirety of time, they most definitely did not go extinct. Ever, and if you thought they did then you're remembering wrong. Again.
In the Jonathan Lethem novel Amnesia Moon this power is possessed by a number of people, which to some extent includes main character Chaos/Everett Moon. The effect is that as you move across the country, you can be thrown from one reality into another that's completely different.

Tabletop Games

Forgotten Realms has a spell that is a very limited version of this—Spellstrike. It completely negates all effects of one recent (in the same or previous round) casting of a spell or use of a spell-like ability, as if it just failed.
- Tome of Magic from 3.5e includes the Truenamer class, who at high levels can (theoretically) unspeak the True Name of someone, literally removing them from the fabric of time.
The Sidereal Exalted boast a technique called Avoidance Kata which, when used early in a battle that turns out to have been a bad idea, allows them to have never got involved. Wounds already inflicted stay, but get a new cause- if you used it after the First and Forgotten Lion never has ripped off your arm, for example, you now will have got it caught in a grinding mill or something.
- They also have a martial arts style that essentially consists of punching your opponent's destiny. Fail to dodge, and you may suddenly be a married carpenter in Nexus.

Video Games

In Ratchet and Clank Future: A Crack in Time, Dr. Nefarious plans to use the Great Clock to create a universe where evil always wins.
Obligatory Touhou example: this is largely the domain of Keine Kamishirasawa. In 8, she devoured the history of a human village so that they can't be affected by the dangers of The Night That Never Ends (obviously, she restored the village later).

Web Comics

The Trope Namer is Erfworld, in which Retconjuration was actually Retconjured into existence.
8-Bit Theater's Sarda uses Retconjuration with abandon and White Mage mucks up his attempt to retconjure the world to how he wants it, but he's more of a straight Reality Warper.
- In fact the quote above isn't quite true. It's more accurately "Re-Write Reality According to Sarda's Whim", as Black Mage learned when he tried to copy the spell.
  - That's part of a Running Joke on Black Mage: Sarda once cast a spell that caused Black Mage to vomit out his innards; Black Mage used his mimic skill to cast a spell that... caused Black Mage to vomit out his innards.
- Thief ~~gets a minor one when he changes the archives so his red outfit was always black~~ has never, ever tampered with the fabric of the universe.
Clockstopper in Super Stupor (a side-comic of Something*Positive); he calls it Nut-Punching Father Time.
- It's also his favorite solution to everything.

Web Original

Germaine uses a "reset button" invented by Foamy in the web series: Neurotically Yours to initiate a series reboot.