Child support. Good luck! It took a couple of decades, but we finally got ours.... In some states there is no statute of limitations for the collection of child support, and they will use the federal systems to track down deadbeats no matter where they are.
In the States you can claim head-of-household on taxes, and the child as your dependent. That will get you some help. You can also do Earned Income Credit if your income is low enough and you have lived in the States for at least six months. That could get you some monetary help . Not sure if the Rump's tax plan changes all of that - I think it might.
Other than that, there's really nothing on a national level as far as financial help for a child that I know about. Depending on the state you're living in, and your income level, you might qualify for the current equivalent of foodstamps, and Medicaid for the child, and perhaps a break on state taxes (if there are any). Good luck - definitely get some sort of court document that stipulates what the absent parent should be paying, as the starter.