My question involves paternity law for the State of: Alabama

13 years ago my husband had a one night stand with a young lady. He was out of town for a couple weeks and when he came back, he found out she was pregnant. He asks her if the baby was his and she said no. She said she is sure the daddy is somebody else. The other man signed the birth certificate and lived with the mom and the girl. Now 13 years later, the other man says he is not the biology father and he think my husband is. My question now, who has to pay for the test? Can my husband say he want a test even when the mother still say she dont think he is the father? If the girl is my husband’s daughter does he have to pay child support back for the last 13 years? It is not like he tried to run but he always been told he is not the father and now everything is not sure no more. I would like to know what his rights would be.
Thaks for the help
sumsum