My daughter was living with her boyfriend and they have a 3yr old daughter. He kicked her out for no reason and has since begged her to come back. She won't do it so now he says he is going to sue her for custody of their 3 yr old daughter cause my daughter sent his mom a txt saying she would never see her granddaughter again. That txt was out of fear, anyway he was in a psych ward this April for trying to kill himself ,I want tto know can he get custody when he has a mental illness

He has to demonstrate to the court that he is the more stable parent able to provide for the 3 year old daughter. A text message is meaningless. It's not as easy as file some papers, go to a hearing and have a judge decide he gets custody. There is much more involved than that. Is he on the birth certificate as the father for starters? If he is "nuts" then it just might be blowing smoke and no real intentions of going to court.

He has a right to ask for at least joint custody unless he can prove the mother unfit. And if not joint, at least visits.

If he was "cured" for his illness the court may review the records. It will be up to you to prove he is a threat.
Even as a "threat" he would stll get supervised visits.