Child support jurisdiction is usually determined by the defendant’s domicile (where he or she is currently living). If you have a child with a military service member, generally you should seek support in the state (and the county) where the service member is currently living (domiciled). However, jurisdiction for deciding child custody is based on the child’s “home state” – or where the child has lived for the six months immediately prior to the petition for custody (or where the initial court order was entered). 
Therefore, if you are seeking child support through the courts, you should file a complaint for child support (or look for a lawyer) in the state and county where the defendant currently lives. If you are seeking custody, then you should file for relief in the state where the child has lived for the past six months (if there is no court order regarding custody already in place). If there is already a court order in place regarding custody or visitation with a child, then you must modify the order in the state where the court order was issued.
If the parties and the child no longer reside in the state where the child custody order was issued, the order must still be respected (as all states must give “full faith and credit” to the orders of other states). However, either party may request (through a petition filed with the state court) that the state where the child currently resides be declared the child’s “home state”. This designation would allow the child’s new state court to modify (or change) the court order entered by the previous state court.
In contrast to jurisdiction over custody of a child, jurisdiction for obtain child support from a parent is determined by a different criteria. Jurisdiction for obtaining child support or spousal support is based on where the person required to pay the support resides. If you are sued for child support in a state where you have minimal or no contact (i.e., you don’t live there, own property in the state, or go there regularly), then you can challenge that state court’s authority to enter an Order compelling you to pay support. The rationale is that it would unfair to be required to defend yourself in that state where you have minimal or no contact. However, if you voluntarily come to the state where the lawsuit was filed, then you may become subject to the state court’s jurisdiction.
A typical example would be if two people have a child together in Virginia and then the mother and child move to California, it would be unfair to the father to have to defend himself in a California court when he still lives in Virginia. If the father comes to California (perhaps, to visit the child), then he may become subject to the jurisdiction of the California court even if he still lives in Virginia. To avoid the jurisdiction of the California court, the defendant would have to file a “Motion to Dismiss” the case for lack of jurisdiction. If he files an Answer to the Complaint for Support, he waives the jurisdiction defense.
 All 50 states have adopted the Uniform Child Custody Jurisdiction Act as state law which provides a set of rules for deciding which state should have jurisdiction to determine custody of a child.