Okay, so y'all remember Black Cat's "I had a kid with you" fakeout from the PS4 game, yeah?
I like to wonder sometimes "what if it wasn't a fakeout?" and then I get to thinking.
The absolute oldest a kid between Peter and Felicia would have to be between 4-5 years old, assuming the two met one another when Peter was just starting college. But for the sake of things, let's say it's been a couple of years since the events of the game, where Miles has only just started being active as the city's second Spider-Man, and Peter's been trying to find a steady job with a high enough salary to both make rent and supplement his crime-fighting budget.
Of course, as befitting of Felicia Hardy, she drops their baby boy on Peter's doorstep with no rhyme or reason given, with nary a sign of the Black Cat in sight, save for the note the kid, one six-year-old Felix Hardy-Parker, was asked to hold onto for mommy. As it turns out, Felicia got herself in some hot water yet again, and so she figured the best place for their son to stay safe was with their father, and that it was better to ask for forgiveness than permission.
So then Peter not only has to balance work, his personal life, and crime fighting, now he has a kid to care for that he thought was real, then thought wasn't because Felicia was being Felicia.
But Peter Parker would rather burn in hell before he'd ever let the kid go hungry or homeless, and dads the fuck up for Felix's sake.
Eventually, I could see Felicia coming back into the picture to once again take custody of their kid after the heat dies down, but then Peter, who would be all too painfully aware of the kind of environment Felix would be growing up in as the only son of a notorious, and above all UNREPENTANT master catburglar, and would do the only thing a guy like him could do, and sue for custody of their child, dead set on giving him the closest thing to a normal childhood that a friendly neighborhood Spider-Man possibly can.