Thread by @SiriuslyCold

Imam Al-Syafie states:
"If a man commits adultery with a woman and gives birth to a daughter, then the man can marry either the woman or his daughter. This is because Allah only makes the mahram relationship based on halal marriage only”. [Al Syafie, Ahkam al-Quran, p. 189]

Imam al-Khatib al-Syirbini said: A woman born of adultery, intentional or not (rape) ... then the law of both of them is halal because it is considered foreign as there is no respect for adulterous sperm. ” [Mughni al-Muhtaj, 4/287].

The final opinion of the al-Syafie school, the seeds resulting from non-sharia intercourse have no legal value.

Qurán:

33:5 Name and call your adopted children after their fathers...

irrespective of how you come to adopt the child. so if a family adopts an illegitimate child, he/she must be named after the biological father, with the attendant responsibilities and rights accorded.

Actually, I was wrong - there is no need to wait for her onset of menses, according to the current translation and understanding of the eddah verse

A better translation of this verse is as follows

65:4 And those of your women who no longer expect menstruation 𝗼𝗿 𝗱𝗼 𝗻𝗼𝘁 𝗵𝗮𝗯𝗶𝘁𝘂𝗮𝗹𝗹𝘆 𝗺𝗲𝗻𝘀𝘁𝗿𝘂𝗮𝘁𝗲, to resolve your doubts, their waiting period is ordained to be three months. ...

This revised translation does not contradict the verses stating requirements for marriage - mental maturity [4:16], consent [4:19], and ability to enter into a contract [4:21]