Will an over the counter DNA test hold up in court?

My son needs to have a dna test done to prove or disprove that he is the biological father to a 5 year old girl. His name is Gavin Triplette and the childs name is Nevaeh Faith Triplette. He does pay child support although he is in arrears at the moment. He went to court for the arrears this morning and arrangements have been made for him to make timely payments until the arrears are paid up and he can continue to pay the normal amount of ordered support from then on. He has never been granted visitation rights and wants to be a part of his daughters life. The child's mother makes it known publicly that the child is not his and we are seeking to remedy this situation. He cannot afford an attorney.