What is the ruling on the action of a father who permitted his children to build above his house, then retracted, and demanded from them more than half of what they built, claiming partnership in the construction and that he wishes to bequeath that to their other siblings?

Therefore, the father's permission to his son to build on his land, without explicitly declaring it a gift, makes it a loan (عاريَّة) and not a valid gift. If the father dies, the son does not exclusively own the land, and the other heirs share in it with him. If the father reclaims his land, he is obliged to give you the value of the standing building. You may agree to become partners in the building. It is advised to be mindful of the father and to treat him with kindness, and to relinquish any right due to him seeking Allah's pleasure.