Is it permissible to attribute the first daughter to the young man who committed adultery with her mother, or to the mother's current husband?

It is not permissible to attribute the daughter to her current stepfather, as adoption is forbidden in Islamic law. As for attributing her to her father from adultery, the majority of scholars do not permit this, based on the saying of the Prophet, peace and blessings be upon him: "The child is for the bed, and for the fornicator is the stone." However, some scholars permit attributing the child born of adultery to his father if he acknowledges him and there was no marital bed (marriage). The child born of adultery is legitimately attributed to his mother and her family, and all the rulings of sonship apply to this attribution.