They are seeing if Florida has a case on this.
Your chances are good if he is employed by a company, and much better now that there is a federal system.
see
How does a court decide which state will hear child support cases?
The law that helps courts decide which state will hear child support cases when parents live in different states is called the Uniform Interstate Family Support Act (UIFSA). UIFSA has rules for each step of the process of getting child support.
Step One: Getting a court to issue the first child support order (establishment);
Step Two: Changing the amount of a child support order when the income of either parent has changed (modification); and
Step Three: Pursuing collection of the order (enforcement).
How does a state court get personal jurisdiction over a parent?
Under UIFSA, a state may get or keep personal jurisdiction over a non-custodial parent if:
The non-custodial parent is personally served (given a copy of documents in person) with a summons or notice (an official document telling the parent that he or she is directed to come to court) within that state;
The non-custodial parent voluntarily agrees to have the court of a particular state hear the matter;
The non-custodial parent fails to contest (object to) the jurisdiction issue;
The non-custodial parent lived with the child in the particular state at any point in the past;
The non-custodial parent lived in the state before the child’s birth and provided prenatal expenses or support for the child;
The child lives in the state as a result of the acts or directives of the non-custodial parent; or
The non-custodial parent engaged in sexual intercourse in the state, and the child may have been conceived by that act of intercourse.
Step One: Getting the First Child Support Order (Establishment)
Personal jurisdiction over both parents required: To hear a new child support case, a court must have personal jurisdiction over both parents. (See How does a state court get personal jurisdiction over a parent? for ways a state court can declare personal jurisdiction over a parent in another state.)
If, at the time the custodial parent first applies for a child support order, both parents and child reside in the same state, the court of that state will enter the order.
If the whole family previously lived in the home state of the custodial parent and child, that state will continue to have personal jurisdiction over the non-custodial parent, even after he or she moves away.
If the court of the custodial parent’s home state does not have personal jurisdiction over the non-custodial parent, the custodial parent may voluntarily submit to the jurisdiction of the court in the home state of the non-custodial parent. The custodial parent would then file his or her application for child support in the non-custodial parent’s home state.
The laws of the state that enters the first child support order are the laws that will determine the following:
How should the amount of child support be calculated?
When does a child no longer need child support?
Should parents contribute to the child’s college education?
http://www.lsnjlaw.org/Family-Relationships/Child-Support/General-Information/Pages/Child-Support-Issues-For-Parents-Living-In-Different-States.aspx#.WSdhfWjyvIU