I would say it probably fits best under applied linguistics, at least according to Wikipedia. Linguist David Peterson has invented a number of fictional languages for TV shows, including the languages used in the show Defiance, and Game of Thrones. He's even written a book about inventing languages called The Art of Language Invention.
Another well known constructed language (sometimes called con-languages) is Klingon, invented in the 80's for Star Trek. And of course there's Esperanto, which has a couple of million speakers and even a few thousand native speakers, supposedly.
Student or Learner