If a child of a Jewish woman has been fathered by a person before marriage, and she marries a Jewish husband before birth and accepts the child knowingly, and the natural father does not claim fathership before court, even if the mother admits that it is not a natural child of her husband.
Supposed the natural fathership is not kept secret (which would usually be the case), who is the official father with respect ot lineage and heritage according to halacha?
Related questions that do not answer this:
Name of adoptive father in the Ketubah
adoption and qualifying for being "officially" considered Jewish
Is a Child Born to Jewish Mother and Father Outside of Marriage a Mamzer?