What is the Sharia ruling regarding the issue of the children of one of the deceased partners benefiting from a room designated for their father in a shared house, while the heirs of the other partner demand their right to it due to the absence of written proof of the designation?

If the contract stipulates common ownership of the house between the two brothers, this includes all its parts. The use of a room or apartment in the house by one of them or his children does not affect this shared ownership, unless there is evidence proving that this room is private property. The general principle is that the burden of proof is on the claimant, and the oath is on the one who denies, as the Prophet, peace and blessings be upon him, said. In case of dispute, the matter is referred to the Sharia judiciary for resolution.