The burden’s mostly off Game of Thrones with regard to Jon Snow’s secret origin, though Season 6’s “Tower of Joy” flashbacks admittedly left some questions.
Considering the efforts Game of Thrones has put toward keeping Season 7 under wraps, it wouldn’t seem likely of them to spoil any major details in print.
You’re warned of potential spoilers for Game of Thrones Seasons 6 and 7 from here on out, but Season 6 finale “The Winds of Winter” only went so far as to confirm Lyanna Stark as Jon Snow’s mother.
External sources cemented Rhaegar Targaryen (Dany’s brother) as the father, though we never quite learned if Jon had a given name.