If the State filed, then it is a Motion to Enforce, commonly called a contempt motion.
It is probably filed in a IV-D court (with an Associate Judge), not in District Court, where custody & visitation (conservatorship and possession & access) are heard.
If you signed a notarized Waiver and returned it to the Office of the Attorney General or the court, you don't have to appear in court. However, you should appear, as the court will issue an arrears judgment & if you don't appear, NCP can claim credit by stating the child lived with him, etc. & you won't be there to contradict him. Also, in a contested hearing, you should be present to identify him.
The process: if he can't afford an atty, the court will appoint an atty for him; that atty may reset the hearing in order to interview the client and prepare for trial. Prior to the trial/hearing, he, his atty, you, and an Asst Atty Gen'l, will have an opportunity to try to come to an agreed order. If not possible, then a contested hearing will ensue.
The order will state a judgment on unpaid child support (arrears) & any unpaid medical support, with a monthly payment ordered for arrears.
Also, he will either be found in contempt, both criminal and civil, with a potential jail sentence of six months. Many Assoc. Judges will find an NCP in contempt, but will defer commitment on the sentence for six months (they will set a date six months in future & at that hearing will examine how well he complied with all the court's orders. The court may also put the NCP on suspended commitmt (probation for up to 10 yrs).
The court may order him to pay lump sums towards the arrears, as well as a monthly payment.
If he is committed to jail, the court should set a 'coercive' amount - the amount of money he has to pay to be released from the civil contempt charge. Although the criminal charge has no coercive, most NCPs are released from jail after paying the coercive/purge amt.
The common effect of these motions appear to be that the NCP behaves beautifully for six months on the deferred commitmts ... at least some money comes into the CP's home during this period. For some NCPs, one experience of staring jail in the face is a curative, and they improve their payment habits.
PS: even if he files for custody, the court should proceed with the Enforcement first.
The NCP will also have to repay the State for atty fees & court costs.
Hopefully they have served him - it would be personal service & he may evade.
Good luck.
PS: if he was served & doesn't show for court, the court will probably issue a Capias, with a cash bond (like an arrest warrant with bail stated).