How to Improve My Chances of Getting Custody of My Child

My question involves a child custody case from the State of: New York City
I have felony record. I served my time and when I get out I was blessed with my baby girl. The relationship with her mother was not working, too much arguments and physical fighting, but I never laid my hands on her. I decided to leave the relationship with her mother to avoid a real problem. She was not the best mother while I was with her and I have noticed that. Things are not changing, its was actually getting worse. I have a new partner and would love to start a new life with her. However, my daughter comes first. I decided to return with the mother of my child to protect her and raise and take care of her.
My question is what can I do to improve my chances of getting custody of my child? I don't want to take her away from her mother but the situation is not getting better. She doesn't take care of her. She would leave her starving till I get home its driving me crazy. I was told that if I leave I may have less chance.lease just give me some advise.

Does Mom know you're using her? That's kind of not good, dude.

An initial custody determination will be based on "best interest". So, let's start at the beginning

How old is the child?
How long have you been with Mom, in total?
Has paternity been established?
Please describe how she doesn't take care of the child.
Do you work? Does Mom work?