What is the ruling on a man marrying his granddaughter, and is it permissible according to Sharia? What is the lineage of the children in this case?

The granddaughter is permanently forbidden to her grandfather by scholarly consensus. Their marriage is invalid, and they must be separated. If they knew of the prohibition, they are considered adulterers and deserve the prescribed punishment for adultery, and the children are attributed to their mother. If they were ignorant of the prohibition (a marriage of شبهة/dubious legality), the charge of adultery and the prescribed punishment are dropped, and the children are attributed to their grandfather. It is incumbent upon anyone aware of this invalid marriage to report it to someone who can annul it and take the necessary measures.