Is the house considered property of the children who paid their father's debt based on his will, or do the other heirs have a right to it?

You may claim from the estate the amount of debt you paid on behalf of the deceased. You are not permitted to take possession of the house, as the father's statement before his death holds no weight. Therefore, what you paid on behalf of your father, you may take from the estate before its division. It is stated in Al-Uqud ad-Durriyah and Al-Fatawa al-Hamidiyyah: "If the executor or the heirs pay the cost of the deceased's shroud from their own money, they may reclaim it from the estate, and they are not considered volunteers. The same applies if the executor or the heir pays the deceased's debt from their own money." And in Al-Bazzaziyyah: "If one pays the debt of the deceased, he may reclaim it from the estate, just as in the case of shrouding." If the remaining heirs agree that you should have a share of the house in exchange for the amount paid, thus becoming partners in it, then there is no objection.