Crazy baby daddy? Help?

So my childs father wants 50/50 custody of our infant but doesn’t have the means to do so ? He also doesn’t want me to have 100% physical and he pay child support (he just doesn’t want to have to provide financially at all let alone 50% it seems). He thinks being in her life is enough. He works part time jobs and barely requests to come visit her. He also attempted suicide twice in October. What would you guys do in this situation ? He even requested a paternity test. He just doesn’t make sense !