Can my son's father get any type of joint custody? I am a single mom (never married) living in the state of MD. My son's father is currently not working and is on disability for his psychological and health issues. My son has always lived with me and I am wondering what the chances are that his father will get any type of joint custody. the child has my last name (father signed Birth certificate after the fact). I don't receive any support from the father and never have. His father doesn't live on his own (still lives with parents) and he doesn't work due to his illnesses. All illnesses are documented by his psychiatrist and doctors as well as his employer since he is on disability thru them.