I don't think the expression, "Who's your daddy?" has anything to do with biology. I think it's in some way related to the old expression "sugar daddy", like, who's paying the bills in exchange for......
Toby Keith's got a song on the "Unleashed" album and it's entitled, "Who's Your Daddy".
"I got the money, you got the honey, let's cut a deal, let's make a plan, Who's your daddy, who's your baby, who's your buddy, who's your man?"