Bran is the 3 eyed Raven now.All The Times Game of Thrones Tried to Tell You Who Jon Snow’s Parents Are
This video explains all the clues between all 6 seasons as far as who Jon Snows parents are. He has a legit claim as both a Dragon and a Wolf. Jon I dont think wants to be King of the North he just wants to live a happy life and find out who his parents are, he's never been about the glory and it showed when Baelish said he declared the battle a Stark victory and Snow shot him down. I think once Bran shows up he will cede the king of the north title to him and let Bran and Sansa run the north while he concentrates on the zombie war coming.
He'll never take control of Winterfell.