A plaintiff can withdraw a suit. The court can dismiss it for non compliance with the court rules. Normally a defendant cannot have a case dismissed without filing a formal motion and notifying the other side. Your son may be able to reopen the case if he can demonstrate that he had no notice of the matter. Your posting is unclear--did your son want to have custody, or to deny custody? If another party is found to be the biological father the court may dismiss your son's suit for non paternity and for lack of standing (he has no legal right to litigate the issue).