Is it permissible for the daughters of the son of an illegitimate child to uncover and put on the hijab in front of him, and is he a mahram to them?

An illegitimate child born out of wedlock is legally and divinely attributed to their mother, according to the majority of scholars. However, some scholars permit attributing the child to the fornicator if the mother was not married. If your uncle was attributed to your grandfather, then he is his son based on the second opinion.

Assuming your uncle was born out of wedlock before your grandfather and grandmother married, then he is your mother's brother only through the mother, according to the majority, or through both parents, according to the other opinion. In either case, he is a mahram to you, and it is permissible for you to uncover in front of him.

It is not permissible to accuse anyone of fornication or to doubt their lineage without four witnesses. Whoever does so without clear proof has committed a grave sin that warrants punishment, and they must repent and seek forgiveness.