In the books, the other Targaryen, Aegon VI, is already accounted for. He just hasn’t showed up in the series.
He’s the son of Rhaegar and his wife Elia Martel. He was supposed to have been killed but it turns out he was switched with another infant by Varys when Gregor supposedly killed him, his mother and sister.
He shows back up with an army and takes several castles in Westeros and lays siege to the Baratheon seat Storms End.
So your 3 dragon riders would be Aegon, Daenerys, and...Jon Snow.
You are assuming the man claiming to be Aegon in the books, actually is Aegon and not just a pretender.
I think it’s telling that all that you mentioned has thus far been left out of the tv series. In in fact the Aegon from the books a pretender... it might have been deemed not even important enough to include in the TV series.
Which would be there is a REAL Aegon out there, and it’s most likely Jon Snow.