Something I've often wondered since seeing a the animated movie with Supergirl and Young Justice Superboy and something that bothers me is that Superman just sends these two to go live on the farm I mean it feels like he shoved the responsibility on to Johnathan and Martha Kent rather then be like "Okay I'm the only other person who can understand what you are going through so I'll help you out." Ironically everybody around Superman seems to be okay with Superman just leaving Cara and Conner at the farm.
This got wondering what would Superman do if he learned he had a son (maybe he got close with a woman while having an adventure off world and in the heat of passion ended up fathering a child) I like this idea because on the surface it might seem like the Superboy dynamic but in truth it would be completely different since as the boy's father he wouldn't just be able to push the responsibility on to someone else. Also it would be fun to see a super hero with all of Superman's powers but with none of his self restraint.
For example his son could openly defy him and get in his face over things like being asked to join the Teen Titans instead of working with Superman in the Justice League by proposing this argument "You said we were partners and now your shoving me off to the freaking kids table? No thanks Old Man! I'm going solo!" I think this would be a funny nickname for Superman especially if it made his feel self conscious and while eating lunch or whatever with Batman and other JL members asked "Bruce do you think we're getting old?"
Not too mention the idea of Clark hearing a knock on his door and finding a pissed off Amanda Waller with his son in cuffs saying "Mr. Kent your son is in a deep trouble he has in the last twenty four hours peed on the Lex Luthor's chair then sent a photo of him doing it to Lex, broken a window to the white house while playing base ball with Kid Flash, and he defaced Mount Rushmore by burning off the faces of the Presidents and replacing them with your symbol and he burned an image of the middle finger into the moon!"
As for why he'd have a son so rebellious toward authority it could come out that the kid's planet was enslaved by Darkseid(who killed the boy's mother in front of him when he was like six) and the boy spent years of his life being tormented and forced to serve Darkseid (who could have been poisoning him mentally against Superman) until he got strong enough to escape. But Darkseid's and Granny Goodness's 'parenting' left the boy with zero respect for authority and a serious temper.
How do you think Superman would react if he learned he had a rebellious son with such a violent up bringing that it made him pretty much an at risk/troubled teen and had a relationship with Darkseid that can be summed up like this.