Does father have to prove paternity of a child if going for custody and never married to mother?

Of course. Generally, if the parents are unmarried the mother has sole custody and control in most states until the father can establish his paternity. Remember, a child's mother can always be identified by medical records. Since the father didn't give birth and he was not legally married at the time of the birth he must establish his paternity by signing the birth certificate at the time of birth (waiving DNA testing rights) which must be done with mother's consent.

If he doesn't sign the birth certificate then he must seek another way to establish his paternity and that is done through a DNA test. A paternity test can be arranged through the court and once established the father can request visitations, custody and set up a schedule of regular child support payments for the child.
Of course. Generally, if the parents are unmarried the mother has sole custody and control in most states until the father can establish his paternity. Remember, a child's mother can always be identified by medical records. Since the father didn't give birth and he was not legally married at the time of the birth he must establish his paternity by signing the birth certificate at the time of birth (waiving DNA testing rights) which must be done with mother's consent.

If he doesn't sign the birth certificate then he must seek another way to establish his paternity and that is done through a DNA test. A paternity test can be arranged through the court and once established the father can request visitations, custody and set up a schedule of regular child support payments for the child.