All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
According to the preponderant opinion of the majority of the Muslim jurists, the lineage of a child born of fornication is attributed to its mother. We explained this in Fatwa 89082. Thus, this girl's mother or her mother's family have no right to disown her. She is kin to them, so they must keep ties with her and they are forbidden from severing those ties.
As for the fornicator [i.e. the man], she is unrelated to him and he is not her Mahram. Hence, his relatives, like his brothers, are also not her Mahrams. As regards their raising her and being kind to her, then this is something good and a means of drawing closer to Allaah The Exalted.
However, if she fears embarrassment of being attributed to her mother, she could be attributed in a general way (by choosing any Muslim surname). For more benefit, please refer to Fatwa 102596.
On the other hand, the one tasked with being the Wali (legal guardian) for the marriage of a girl born of fornication is the Muslim ruler or his representative, due to the saying of the Prophet, sallallaahu ‘alayhi wa sallam: “The ruler is the Wali of the one who does not have a Wali.” [Ahmad, Abu Daawood, At-Tirmithi and Ibn Maajah]
We note here that the Awliyaa’ [pl. of Wali] are the woman’s blood relatives through her father. The relatives through her mother are not her Awliyaa’ and are thus not authorized to give her hand in marriage.
Allaah Knows best.