Wa `alaykum As-Salamu wa Rahmatullahi wa Barakatuh
The view of the massive majority of Muslim scholars is that a child who is born out of wedlock cannot be attributed to his father. This is based on the hadith of ʿĀ’ishah (may Allah be pleased with her) who reported that the Prophet (peace be upon him) said, “A child belongs to the wedlock and the adulterer has nothing.” (Al-Bukhari and Muslim).
Therefore, he cannot inherit from her biological father nor the father can inherit from her. She is attributed to her mother and the relatives of her mothers can inherit from her.
For marriage guardianship, this biological father cannot be a recognized father for her. She does not have to take his permission when she gets married.
Almighty Allah knows best.
Views expressed by hosts/guests on this program (live dialogue, Facebook sessions, etc.) are their own and their appearance on the program does not imply an endorsement of them or any entity they represent.