(spoiler, probably still)
There was a fan theory that Jon Snow wasn't Ned Stark's bastard, but the son of Lyanna Stark and Rhaegar Targaryen and the season six finale confirmed it. Currently, only Bran Stark knows this and Jon has apparently been "crowned" King in the North as the last known and eldest son of Ned. Of course, if his true parentage gets out, then it could lead to questions of who the true ruler of the North is. Sansa has the stronger claim as Ned's daughter and is considered (at least according to the GoT wiki) to be Lady of Winterfell. Jon does have a claim through his mother, but Sansa's is stronger as the daughter as and sister of the last two Stark Lords of Winterfell, respectively.
Of course, the question is whether or not the Northern Houses would accept a woman as Queen? House Mormont has been lead by two women so far and Lyanna Mormont seems to be widely respected by the other Houses, so it's entirely possible.
As for Jon, having the blood of Rhaegar gives him a stronger claim to the Iron Throne than his aunt, Dany. On the other hand, he's still a bastard and she isn't. He was legitimized by the Houses of the North when he was crowned King of the North, so it stands to reason that the same could very well happen there.
(Pic via HeroPress)
