can i travel with my son who is in my custody with his father permission?

Travel in custody cases depends on the order and federal law.  While the parties can generally agree to whatever they want, the first place to look is the court order.  If the order restricts travel, the best way to proceed is to modify the order to allow for such travel.  Also, you will want something from the father confirming his permission and clearly spelling out what travel is allowed so that you avoid any claim that you acted outside the agreement. When traveling outside of the U.S., the Department of State has forms which must be signed by the non custodial parent authorizing the travel.