Is it permissible for a father to open a business in his son's name, with the capital provided by the father, a fixed profit for the son, and the remaining profit returning to the father?

The type of transaction between the questioner and his father in the project must be clarified. If it is a lease (ijarah) for his work with a known monthly wage, then it is valid. However, if it is a partnership for a fixed amount of profit, and not a common percentage, then it is impermissible due to the uncertainty of the wage. But if he has a known percentage of the profit, along with taking a monthly amount as an advance, and then the accounting is settled later, this is permissible.