The birth certificate correction form cannot be used to add/remove a father/second parent to/from the birth certificate.
Add a father/second parent to a birth certificate
To add a father/second parent to a birth certificate where a father/second parent is not currently listed, complete and submit the Voluntary Acknowledgement of Parentage form | In Spanish.
Remove a father/second parent from a birth certificate
To remove a father's/second parent's name from a birth certificate, you must submit a copy of certified court documents showing paternity/parentage determination with a completed data worksheet for the new birth certificate.
Court-determined paternity/parentage documents are required to add, remove or change a father's/second parent's name on a birth certificate when another individual is shown as the parent of the child on the original certificate.
A new certificate may be prepared only when a determination of paternity/parentage is made by a court of competent jurisdiction or following adoption. A divorce decree is not acceptable evidence regarding paternity/parentage.

Report of paternity/parentage determination (for court use only).

Certified copies of acknowledgement of parentage
A certified copy of the acknowledgement of parentage can be used as evidence to establish paternity/parentage for agencies such as the Social Security Administration.