A word for this type of sequel

Question

Let's say someone writes three novels, two of which are sequels.

The 1st novel establishes the main plot elements that are used in the second novel.
The 2nd novel (the sequel) is written in a manner that it continues from the plot of the 1st novel with the same characters and other elements as an intended sequel, but the author declares that it's not the actual continuation of the plot of the first novel and goes on to state that the 3rd novel would be the official sequel.
(Some background on this could be that the author intended for the 2nd novel to be the true sequel, but rolled back on their decision after generating negative reactions from readers and wanted to create a different sequel that still takes on after the plot of the 1st novel.)

What would the 2nd (discarded) novel then be called?

Answer 1

It's a non-canonical sequel. While it's unusual to for things to be retroactively made non-canon, it happens, with a prominent example being Star Wars Legends:

Aside from film and television adaptations, which have been directly adapted into other mediums, such as novelizations, comics, and video games, the franchise has been expanded into original storylines. Except for direct adaptations of the films, only works released since 2014 are considered part of the canon (with the non-canonical works rebranded as Legends).
_{Star Wars expanded to other media}

Answer 2

There appear to be a number of -quel words formed by back-formation from sequel.

According to this page:

• a sequel is a story that takes place later in the same imagined history of a story using many of the same characters and settings

• a prequel is a story written or published after a certain other story, but whose events take place earlier in the same imagined history

• a paraquel is a story that takes place at the same time as another story with the same or similar characters

• an inquel is a story that takes place during a gap in another story’s narrative.

• a circumquel is a story that takes place partly before and partly after another story.

• when a story is a prequel to one book, but at the same time a sequel to another, we are reading an interquel.

The page cited provides several examples that may help you decide where your situation fits, but what you describe sounds most like a paraquel. (Or, at least, the author has decided to make it one.)

Answer 3

It's a *nonquel.

1. This week our mancrush will reteam with Wain for the communal comedy "Wanderlust" (costarring Jennifer Aniston), and later this year he'll reprise his "Knocked Up" role alongside Mann in Apatow's nonquel "This Is Forty." (mtv)

2. TERMINATOR SALVATION: A 'Nonquel' ("The Movies With Lim Chang Moh")

3. The film (Fierce Creatures, 1997) had many similarities to "A Fish Called Wanda" -- the same principal cast was used, several of the other actors from the earlier film also appeared, and there were lines and gestures that were seen in both films. Cleese referred to "Fierce Creatures" as a nonquel … (funtrivia)