Is the biological father of an illegitimate daughter mahram to her?
If not, does she have to do Hijab from him? And does she not inherit property from him?
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According to most scholars (except for the Shafi'is), she is mahram to him but she still does not inherit from him nor is she attributed to him (in all four Sunni madhabs).
The prohibition about daughter also applies to the daughter of the son and the daughter of the daughter. There is, however, a difference of opinion in regard to a girl born of an illicit relationship. Imam Abu Hanifah, Imam Malik and lmam Ahmad-bin-Hanbal (may Allah bless them all) are of the opinion that she too is unlawful like the lawful daughter, but Imam Shafi 'i does not consider an illegitimate daughter unlawful. But the very idea is repugnant that one should marry a girl about whom one has the knowledge that she is of one's own seed.
Tafsir Al Maududi 4:23
According to the majority of scholars, he is not considered her father and so he has no rights over her or duties towards her, neither does she to him. She does not inherit from him, nor does he inherit from her. She is not attributed to him, rather she is attributed to her mother and her lineage goes through her mother.
This is based upon the hadīth in Bukhārī and others:
The child belongs to the one on whose bed it is born.