Nothing. As long as you are native born or you have come legally.
If You’re born here you’re a citizen. What do anchor babies, family unification, and illegal aliens have to do with it. If you’re here illegally and have a kid you can go back with your kid or without your kid. Most of those kids will have dual citizenship so their parents can decide. If you leave your kid your welcome to try the legal route,
Plenty of visiting women have their kids here on purpose and then go home with the kid.