What if Voldemort had a child?
Ideally it would be before he turned evil, and after he graduated. So about 17/18 roughly, (And I’m going to assume that his baby mamma is of the same graduating class) but before he went looking for the relics of the old Hogwarts founders relics. So about 1945.
Now suppose that there were rumors going around at that time that Tom Riddle, Hogwart’s golden child, is delving into dark magic. Dumbledore might convince the mother to go into hiding, in case people find out about his illegitimate son. And what better place than the one that Riddle would never go to? That’s right- Muggle London.
So time skip to when the child is older. Presumably, his mother has forsaken all forms of magic to blend in with muggles; however, considering the child’s strong lineage in magic, it wouldn’t be long until the child got their Hogwarts letter. It would be 1956 by the time that the child is eleven so imagine the horror the mother feels when they receive their Hogwarts letter. (I would be a concerned parent for sure considering the only person who would know that they aren’t muggle-born is Dumbledore.) It was the the in the middle of Voldemort’s rise to power, and this kid, who I would imagine didn’t know that magic even existed, gets introduced to it in a time where muggle-borns were disappearing without a trace. Not to mention that they were probably told to hide their ability to speak Parseltongue. (Can you imagine explaining how a MUGGLE-BORN can speak to serpents, a skill only held by descendants of Slytherin?)
Well time skip again to 1963, when said child graduates from Hogwarts, the beginnings of a wizarding war are on the horizon. It would probably be wise to keep their head down and maybe take a ministry job. But I would like to think that they would become an auror and fight the dark arts, like Tom Riddle did when he first applied to Hogwarts as a Defense Against the Dark Arts Teacher.
Imagine Voldemort battling aurors in the first Wizarding War and in the middle of battle he sees someone that looks remarkably like him. But how could Voldemort see himself in someone so beneath him because they’re a muggle-born? At the final battle at Hogwarts, he sees the same person, who reminds him of himself so much for some reason, fighting off death eaters and sees Nagini try to sneak up on them. And to his astonishment, they speak to her in Parseltongue- something only he and Harry Potter can do.
And shortly after Voldemort sees them hug a child, a young boy in Slytherin that looks like him when he first opened the Chamber of Secrets- only die by the hands of Potter a few minutes later.