Citizens of the United States of America enjoy certain rights under the U.S. Constitution and State Laws. Non-citizens have access to some of the protections established under the law but not all of them. With regard to child support non-citizens have certain protections but are also held to certain standards. Not being a citizen of the United States does not mean you are not entitled to child support and it does not prevent the other parent from seeking child support from you.
Child support obligations are established and controlled by the laws of the individual States. There is no federal support laws. Each State has its own rules and you should consult a lawyer in that State to get more detail regarding the information provided here. Which State laws you are operating under generally depends on which State has jurisdiction over the child. If your child is residing in the United States then the State the child resides in should have jurisdiction over child support. There are various factors that determine whether the courts of that State have jurisdiction but in general if the child has resided in that State for at least six months some court in that State should have jurisdiction. If the child resides outside of the United States of America then the State court where the other parent resides should have jurisdiction over child support disputes.
If you are the non-citizen and are the primary care giver for your children you should be entitled to financial assistance to raise your child in the form of periodic payments from the other parent under the laws of which ever State has jurisdiction. If you cannot reach an agreement on an amount of child support with the other parent they you will have to file a law suit in the appropriate court. Once you file suit you will have to have notice of the suit served on the other parent. Notice laws are very particular. Everything must be done perfectly or any ruling issued by the court will be invalid if challenged. After serving the other party the court will require that you allege and prove that the other person is in fact the parent of the child. You may also be required to prove that the child is a citizen of the United States. The court will then want to see the income of one or both of the parents and will establish the amount and manner of payment of child support.
If the other parent is the non-citizen your biggest concern is getting service of process or notice of the lawsuit to them. If they are in another country this can be difficult to impossible. Most States have options for dealing with people that are avoiding service, but again the laws regarding service are very strict and you will probably need a lawyer who is familiar with this area of the law. If the non-citizen parent resides in the United States and you can get notice served the court will order them to pay. If they fail to pay they face the same consequences as anyone else in violation of court ordered child support as well as the possibility of deportation, denial of a visa or denial of citizenship.