Did the man err by donating his sperm to a sperm bank? Will he be held accountable for that? Do these children have any material or moral rights over him?

You must repent and seek Allah’s forgiveness, for this action of yours leads to the loss of honor and lineage, and it contravenes all divine laws that safeguard the six necessities. The fertilization of a woman's egg with the sperm of a man who is not her husband, the substitution of human sperm with that of another, the selling of sperm, and the establishment of sperm and embryo banks are unanimously prohibited and lead to the mixing of lineages and the disruption of the family. The Prophet, peace and blessings be upon him, forbade the earning from a stallion's stud service (ʿasb al-faḥl), which is the fee taken for breeding a male animal. So how much more severe is the selling of human sperm, which results in corruption? These individuals who were created from your sperm are not of your lineage, and they have no rights upon you, because this sperm is considered wasted. However, they are treated like the children of adultery in terms of the prohibition of marrying their daughters.