Is a girl who was born after her father divorced her mother, and without having consummated the marriage with her, considered my legitimate sister, and what is the ruling on mixing with her and shaking her hand within the framework of legitimate brotherhood, and is it necessary to investigate the ruling of li'an, which has not been proven to have occurred, knowing that this will expose the girl, and that those with rights have waived their rights?

The child born six months after the marriage contract is legally the husband's son and can only be disowned through li'an (oath of condemnation). The man must disown the child through li'an if he knows with certainty that the child is not his, such as if he did not have sexual intercourse with his wife, or if she gave birth to the child less than six months after intercourse and the child lived, or more than four years after intercourse. However, if the child is born between six months and four years after intercourse, and the wife did not observe the waiting period (istibra') with a menstrual cycle thereafter, then it is forbidden to disown the child through li'an.

If li'an does not occur, the girl is attributed to your father and inherits from him. If you are not certain about your father's li'an, then treat her as a relative, not a sister. This means maintaining ties with her and being kind to her, but do not be in seclusion with her, nor travel alone with her. It is also preferable not to shake her hand, as a precaution, based on what is stated in the hadith that "the child is for the bed" (i.e., attributed to the husband of the marriage bed). Also, Sawdah was commanded to observe hijab from a brother who was attributed to her father, but the Prophet (peace be upon him) saw a resemblance to the fornicator, so he commanded her to observe hijab as a precaution.