Petition for (Custody) (Visitation). Where to File for Custody.Custody cases are usually started in Family Court. Complete General Form 17 to petition for custody or visitation. Family Court handles custody, visitation, and guardianship of children. It also issues Orders of Protection. In this video we'll cover three terms to always include in the plan the steps to file for custody in New York and how to modify a custody agreement. You should file the custody petition in the Bronx. A custodial parent may file a petition with their local child support agency. In general, the child must have resided in New York State for 6 months or more before a custody petition may be filed.