Baby's Father?

So the baby's father & I are no longer together. He is such a bad person and he is not fit to be a parent. He doesn't work, he's always going out, hanging out with his friends & is always drinking. I don't see him fit to care for another life. I was told that if I didn't put him on my baby's birth certificate that he wouldn't have a say in anything on the child's life. But I was worried that if he tries to get custody he could get a DNA and win. I'm not sure & I'm super worried.