Go to the Civil Registrar Office on the City where the Child is Born and ask for a Form required by NSO.
AS per NSO:
The name of the father of the illegitimate child may be indicated on the birth certificate of the latter whenever the former executes an affidavit of admission of paternity, provided that such affidavit shall not affect the naming of the illegitimate child. (Opinion of the Civil Code Revision Committee, September 23, 1988)
The affidavit mentioned in the immediately preceding paragraph, if executed by the father shall be permanently attached to and shall form part of the birth certificate of the illegitimate child. the birth certificate in such a case must have a remark "With Attached Affidavit of Admission of Paternity" impressed with a rubber stamp at the upper left-hand margin and duly signed by the local civil registrar or authorized civil registry personnel.
Illegitimate children falling under this classification who were not registered within the prescribed period of registration shall comply with the requirement of delayed registration of births. (Section 4 Circular No. 89-13 dated July 17, 1989)