Fictional Field of Science

The world is full of wonderful things, with countless new discoveries paving the way to whole new scientific fields. A hundred years ago, fields like genetics, quantum physics and computer sciences were either almost unheard of, or simply did not exist yet. Go back a hundred years more, and more scientific disciplines we know today did not exist yet.

Science Fiction writers have picked up on this, and creating a whole new scientific field has become a common method to show that this is The Future. It also helps legitimize their Applied Phlebotinum (especially if it's a Minovsky Physics-type one) by telling us that there's a whole scientific field dedicated to it, making it feel more like an ingrained part of the work's setting.

May or may not be a fictional extension of an already existing Real Life discipline. Compare/Contrast Fantastic Science, which is when the new "science" studies/explains the supernatural. Not to be confused with Fiction Science.

General

 * So many sci-fi works across the various media forms have Psionics, the "scientific" study of Psychic Powers, that listing them all would overshadow the rest of the examples.
 * Some Speculative Fiction settings have fictional social sciences such as Asimov's pyschohistory, which allow for not only description of social situations but far more accurate way of predicting future human actions or large scale developments in human society than is possible at present.
 * Many forms of Faster-Than-Light Travel will be associated with some sort of supporting field of science, often some sort of variant of Subspace or Hyperspace in their name.
 * Humans who study alien planets and lifeforms will often add the prefix xeno- (from the Greek word "xenos" meaning "outsider", "foreigner" or "stranger") to the name of an existing science, resulting in designations like xenobiology, xenoarcheology, xenolinguistics and so on.

Anime and Manga

 * Mobile Suit Gundam gives us Minovsky Physics, a branch of (particle) physics dedicated to the eponymous Minovsky Particle.
 * Neon Genesis Evangelion has a passing reference or two to Metaphysical Biology, which is implied (both from in-universe clues and from the name) to be the "science of souls". We never get a proper explanation of what exactly it is about, though.

Comics

 * In the Marvel Comics Civil War series, Reed Richards helps Iron Man with the Superhuman Registration Act because he'd calculated the future of society by Psychohistory. In one issue, he explicitly stated that he'd been fascinated by Asimov's description about the discipline as a child, and as a result, had actually invented it IRL. He and Johnny even went and brought the Thinker to his HQ and showed him his equations, as aside from Reed he was probably the only one who could understand them.

Literature

 * Isaac Asimov has several of these:
 * Psychohistory, developed by Hari Seldon, in the Foundation series.
 * Robopsychology, in his robot stories, which Susan Calvin pretty much invented herself.
 * Robotics itself. Since Asimov's stories predated the development of robotics as a science, when he had characters in his stories as scientists working with robots, he used the word "Robotics" to describe it thinking the word already existed. It was in fact the first publicized use of the word, and Asimov is credited with its creation. Psychohistory is another word Asimov invented that is now a real scientific term, although its use in psychology is different to that in his stories.
 * From the Anita Blake series Preternatural Biology, the study of preternatural (magic/paranormal) creatures, like dragons, yeti, vampires, what have you. It's actually portrayed fairly realistically (for instance dragons aren't magic exactly and don't breathe fire, they are giant lizards, many of them hunted to extinction, and trolls are a kind of primate closely related to humans).
 * Gordon R. Dickson's Childe Cycle - The Exoctics have a social science called ontogenetics that allow them to percieve patterns in human history and to a certain degree predict which individuals and events will be key points in the evolution of humans to a higher state of being. While the exact details are intentionally left vague, it is said to involve calculations that take into account every person in all the world, as well as how institutions and societies shape the pattern of history and human evoltion. One component of the science is the idea that certain individuals have an unusually large impact on the pattern of history. Gordon R. Dickson often uses this as something of an Lampshade and in-universe justification for the fact that his Main Characters (some arguably rising to the level of The Chosen One) all play a major role in the movement of the Myth Arc toward his planned final ending, which sadly was never revealed in full because of Author Existence Failure.
 * Harry Potter has Herbology and Magizoology, the magical equivalents of botany and zoology.
 * Stanislaw Lem's novel Solaris has "solaristics", the study of the titular planet.
 * Dan Brown's Robert Langdon is a professor of "symbology" -- which isn't a field of its own so much as a tiny sliver of anthropology.

Live Action TV

 * Star Trek has Warp Theory, Temporal Mechanics, Exoarchaeology ("Exo-" as in "Exoterrestrial"), Exobiology, Exogenetics, and Exochemistry.
 * The Stargate Verse has Wormhole Physics.
 * As does Farscape.

Tabletop RPG

 * Shadowrun has Parazoology and Parabotany, the scientific study of Awakened (magical) animals and plants, respectively.

Web Comics

 * The webcomic Artifice features a robopsychologist.