What is the ruling on this child, and is he considered an illegitimate child, given the invalidation of the marriage contract and the discovery that his mother is an illegitimate child, and does that affect his lineage?

The child born from a void marriage is not considered illegitimate (born out of wedlock) and is attributed to his father as long as the father believed the marriage to be valid. This is because the child is affiliated with his father's lineage, and they inherit from each other by the consensus of Muslims. The child born out of wedlock is not held accountable for the sins of his parents, and if he performs righteous deeds, that [his origin] will not harm him, based on the saying of the Messenger of Allah, peace and blessings be upon him: "There is no burden on the child born out of wedlock from the sins of his parents, and no bearer of burdens will bear the burden of another." The narrations that seemingly contradict this, such as "The child born out of wedlock is the worst of the three," are interpreted as referring to the child born out of wedlock who acts upon the deeds of his parents.