a.k.a. Outlying Canon, Fanon Expanded Universe, Canon Compliant Fanwork
Sometimes when writing a Fanfic, instead of pulling the more common fare of an Alternate Universe Fic, a fan may write a story that is supposed to fit within the borders of, and does not contradict, the official canon.
A Pseudocanonical Fic presents itself as an in-between episode of the series with its events taking place between installments of the work or, if the writer is talented, within them but expanded upon or with a detailed perspective. Alternatively, it may be the events as presented expanded upon in light of a twist the author has added that hasn't been confirmed nor denied in canon. Additionally, no irremediable event such as the death of a character will happen in it, because their aim is to write a story that has the fewest chances to ever be contradicted in future official works.
This mostly happens for incomplete series. In some cases the season or arc (or even entire series) in which the fic takes place ends without discrediting the events written by the fans, and these are sometimes adopted by other fans as part of the unseen canon of the series. In rare cases the ideas will be picked up by the series, or even revealed to have been part of the creators' plan and fans just happened to think it up, too.