According to Hong Kong's Next Magazine, the birth certificate records that Marcus Cheung was born at Hong Kong Sanatorium & Hospital on Nov 18 last year.
However, the father's name was not stated.
According to Hong Kong law, it means the child has no legal relationship with the biological father and will have no rights to the latter's estate.
Cheung, 38, has two sons - Lucas, 11, and Quintus, eight - from her five-year marriage to actor Nicholas Tse. The couple divorced in 2011.
Speculation on her third son's father has ranged from a 65-year-old Singaporean tycoon, a 50-year-old Chinese magnate, and Tse to actor and director Stephen Chow.
The magazine reports that Cheung sent Marcus to Vancouver, Canada after he was born so that her half-sister Dai Pek Chi could take care of him.
The two women enjoy a close relationship and Cheung had previously sponsored Dai's studies in Canada.
Cheung had also taken Lucas and Quintus to Canada for a period after her divorce from Tse. Dai helped to look after the two boys when Cheung worked.