How can non married father get custody of his son to go back to NYC from NC

Under New York law, unless the mother consents (in writing, I would advise) to the move, your son must bring an action for full custody of his son and for leave to relocate out of state, in the family court in the county in which the child lives. If that's in North Carolina, the action must be brought in North Carolina. Beyond that, I can't advise you- I only practice in New York. But family law tends to be fairly similar from state to state and in this area, as in most everything in family law, courts decide based upon "the best interests of the child."    In New York as well, the father would have to prove it's in the best interests of the child that he get full physical and legal custody, and once that's granted, that the court grant him leave to relocate out of state. Assuming everything you said is true, your son's petition would likely be granted if it was brought in a New York court. But again, a New York court only has the ability to give him leave to move to another state, but no authority to order a child who lives in North Carolina to relocate to New York. Only a North Carolina judge can do that, if the child lives in North Carolina.