Do my siblings have a right to the price difference of the apartment I bought for less than its value, given that my mother lives in it, knowing that the reason for this is my father's rental of it before his death?

If the old lease agreement is open-ended, it is invalid and must be terminated, and the apartment returned to its owner. The owner is not obliged to reduce the price of the apartment for the tenant. If the owner is forced to sell because the tenant refuses to vacate, the sale is void due to lack of consent. It is not permissible to obtain a discount from the owner except with his consent, for the Prophet, peace and blessings be upon him, said: "The property of a Muslim is not lawful except with his willing consent." Your siblings have no right to this discount, nor do they have the right of pre-emption to purchase the apartment, because they are tenants and the tenancy has expired. The notion that the discount can be inherited is incorrect.