CHILD SUPPORT who should pay DA STATE OR DA Parent

In the case of child support, if a man is wrongly accused of fathering a child and has to pay child support, but then finds out 10 to 15 to 20 years later that it's not his kid who should be responsible to pay back the child support, should it be the mom or should it. Be the state because the state gets the majority of the child support money in processing fees and things like that, so should it be a fifty-fifty or should they split it and pay it back the same way they took it?