Birth Certificate

I have a 7 week old baby. The father and I are not married. At the time of delivery I did not let him sign the birth Certificate. What rights does he have?

Would he not have the right to require a DNA test and sue for custody? Are you not planning to ask for child support? Is this going to be yet another baby growing up fatherless in the world because you don’t want him having any rights, but not thinking of the right of the child which is to have TWO parents participate in their life.