How do I handle custody for my child with the father living in a different state?

You don't say how old your child is but obviously a school age child cannot live in two different states and no court would order such an arrangement. You need to file a petition for custody in family court. If the dad also files for custody the court will award custody to the parent in the state in which the child has the strongest family ties and in which the child's education, activities and medical care takes place., The standard is always the best interests of the child.