What is the ruling of the Shari'ah on forging the date of a contract of sale for an apartment to himself, after the death of the father, so that it would be in his name without his siblings, knowing that the father had issued him an official power of attorney to sell the apartment to himself and to others?

The agency is nullified by the death of the principal, by consensus. What you did by forging and registering the apartment in your name is wrong. The solution is to repent to Allah and restore the matter to its rightful legal status. If the apartment belonged to your father at the time of his death, it is for his heirs after his death. If he had debts, those debts are to be paid from the estate, because debt takes precedence over the right of the heirs. If he left nothing but the apartment, it should be sold, its price used to pay the debt, and the remainder divided among the heirs. If there is a dispute or conflict among the heirs, the resolution of the matter is to be referred to the Sharia (definition) court or to those qualified to judge from among the people of knowledge.