Is it permissible for a father to give the zakat of his wealth to his unemployed nephew, on the condition that the nephew returns one-third of the profit from the project he will establish with this money, knowing that the father will pay zakat on this one-third, and that his nephew does not treat his mother well except when he needs money?

If your paternal cousin is poor, it is permissible to give him zakat. Once he receives it, he owns it and can dispose of it as he wishes. It is not permissible for the zakat payer to take a portion of the profits generated from the zakat money given to the poor person, because as soon as the poor person takes possession of the zakat, the money becomes his private property. Therefore, the zakat payer must return whatever profits he took to the poor person.