What is the legal ruling regarding a girl whose mother claims she is the daughter of the questioner's father from an illegitimate relationship (based solely on a Fatiha recitation ceremony), with no proof other than the mother's claim? Is the girl considered a half-sister? Does she have any legal rights? And what should the questioner do concerning this matter?

A legitimate marriage has its conditions and pillars. Merely reciting the Fatiha does not validate the marriage, and consequently, cohabiting with the woman based on it is considered illicit sexual intercourse (zina). The child resulting from such a union is attributed to their mother, inherits from her, and she inherits from them. Their maternal relatives are their kin. They have no relation to the fornicator or his children; thus, they do not inherit from them, nor do they inherit from the child. Using medical tests to prove the child's paternity to the fornicating father is legally meaningless [in Islamic law]. If a dispute arises with the woman, keep the matter away from your sick mother.