This will be a long prompt: Basically, Haytham really is an assassin and his cronies are actually part of the Creed too. They work alongside the waning Achilles to stop Washington and his group that are working with the Templars and pretty much the first part of the game is canon up to Haytham's reveal of the "Father of Understanding" junk.

So Haytham still hooks up with Ziio but learns that she's pregnant and sticks around to be with her. Unfortunately, Ziio still dies and Haytham takes Conner from the ruins of his village and back to New York to live with him and the other assassins.

Cue amusing and lighthearted situations with Conner's uncles and his dad-

Charles Lee, a motherly-hen type that's really strict with Conner's studies but still showers him with hugs.
William Johnson, trying to teach Conner his people's history (and annoying the others with his blathering.)
Thomas Hickey, the cool uncle that gives Conner beers and ogles women in front of the kid.
Benjamin Church, uh... the old doctor guy that's usually being a pain in the butt?
Jonathan Pitcairn, teaching war tactics to Conner (much to Haytham's annoyance.)

Tl;dr- Haytham, still an assassin, takes young!Conner to live with him after Ziio dies and the other Templar guys (that are also assassins) teach Conner the ways of the world but with zany situations coming up.