Affidavit of Attorney for Child in Support of Motion for an Order for Sibling Placement or Contact). Where to File for Custody.Custody cases are usually started in Family Court. 1. Fill out a child support modification petition. 2. File the petition with the Family Court that most recently established your order. 3. A blank Response to Petition for Custody and Support of Minor Children (form FL-270) must be served on the respondent with a copy of this Petition. The clerk will help you file a petition for custody. Either parent can file a petition for final custody at any time. A custodial parent may file a petition with their local child support agency. Follow these steps to change a parenting time, custody, or visitation order.