What is the ruling on selling my share of my father's inheritance to my brother, given that the apartment is rented and subject to a late fee, and that my brother will pay me my share from money whose origin is usurious bank interest?

If the apartment is rented under the old rental system based on perpetual and inheritable tenancy, then this system is invalid and the contract is Islamically corrupt. The apartment does not belong to your father for you to inherit, but rather to its original owner. Therefore, you have no right to sell a share of it to your brother or anyone else. Instead, it must be returned to its owner, or rented from him with a valid contract. Whoever wishes to buy it should purchase it directly from the owner.