Is it permissible to attribute the child to me if medical tests prove she is my daughter and the one who registered her in his name does not object? And do I sin by denying the matter for fear of scandal and the destruction of my home?

An illegitimate child is not attributed to the fornicator but rather to his mother. He is not legally affiliated with him, even if the fornicator claims him. DNA testing is not considered proof for establishing or disproving lineage. It is permissible to deny fornication and use allusive statements (al-ma'arid) in the denial. It is permissible to deny the paternity of the girl, as she is not legally his daughter. A pregnancy conceived before marriage is not legally attributed to the husband, even if it is from his semen or if he married her mother before the birth.