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.

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.)

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.

I'm not quite sure which of these would fit the situation you describe, but you have a number of choices.

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.