The show did not outright reveal who the father was in Season 6, but the Season 7 finale finally made it plain when Bran went back to that scene in the Tower of Joy and we heard Lyanna say that Jon Snow’s true name is Aegon Targaryen, the trueborn son of Rhaegar Targaryen...
James Grebey
but Season 6 finale “The Winds of Winter” only went so far as to confirm Lyanna Stark as Jon Snow’s mother. External sourcescemented Rhaegar Targaryen (Dany’s brother) as the father, though we never quite learned if Jon had a given name. ...
In hindsight, George R.R. Martin had been laying clues for Game of Thrones fans about Jon Snow's real parentage for years.