TMZ has obtained a copy of the birth certificate of the boy Arnold Schwarzenegger fathered ... and he's not listed as the father on the birth certificate.
As TMZ reported, Mildred "Patty" Baena -- who worked as a housekeeper/assistant for Arnold and Maria -- is the mother. She listed her then-husband, Rogelio Baena as the dad.
Baena used a different last name on the birth certificate -- Pena.
The boy was born on October 2, 1997, which now makes him 13. He was born at Saint Joseph's Hospital in Burbank, CA.