What is the Islamic legal ruling on possessing an apartment and claiming its ownership based on a document from the grandmother, issued four years before her death, while one of the heirs objects, and the father and uncle testify to the transfer of ownership, and given that the value of the apartment is less than one-third of the estate?

The action taken by the grandmother, Heba, is a valid gift due to the act of possession, and it is not a will. Even if we assume it were a will, it would be valid for a non-heir and within the limit of one-third. This gift is proven by the heirs' ratification, or by an authenticated document, or by the testimony of two men, or one man and two women, or by one witness and the claimant's oath; this is based on the Hadith (definition) of Ibn Abbas that the Messenger of Allah, peace and blessings be upon him, "judged based on an oath and a witness." Your uncle's testimony is acceptable for you, and the apartment will be established by it along with your oath. However, a father's testimony for his son is not accepted, nor vice versa.