Need Help. Going through a divorce. We have a baby together who has only lived with me, now he wants custody..?

My husband and i have never lived together nor has he taken care of our child. I did file for child support and after i filed he started giving me a small check $100 every time he gets paid. Before i filed for child support all he did for the baby is buy formula maybe twice a month. All the babies expenses were handled by me alone. How will a Texas court see this situation? Does he have a chance at getting custody? From September to now he has only visited the baby 12 times.