Is it permissible for me to apply for the housing allowance by listing my information as a tenant when I am not, knowing that I give the money to my father and live with him?

It is not permissible to resort to trickery to obtain a housing allowance if the responsible authorities stipulate that it be disbursed only to those who do not own a residence. If the questioner meets this condition, then he may take it. Otherwise, it is not lawful for him to resort to trickery to take what he does not deserve. He should remember that "sin is what wavers in the chest."