Can someone please give me advice as to whether or not I should file for custody in court or leave things as they are?

My son was born May 3, 2013, his father was not in his life until March 2, 2014, and only because I contacted him. He then decided to create a relationship to get me to cancel a court order for child support. We have never lived together. He has done anything that he can to try and make it seem as though I am unable to care for my child just to get out of having to pay support. My son has my last name and only myself on the birth certificate. During the 4 months that we dated, he was rarely around. He has done nothing to support my child or to establish any kind of realtionship with him. Although I can support my child on my own without the child support, the support would make things a bit easier. Should I go forward with the support issue and leave the custody issue up to him to fight for, or would it be in my best interest to leave things as they are. I should note that I am fearful of my child's well-being if left in his care as his father has high anxiety issues & no med care.