Is it permissible to withhold a sum of money from the father in exchange for what he took from the son, while paying the remaining difference of the father’s debt to the son? And what is the ruling on the money and profit resulting from the partnership between them?

This matter requires detailing to ascertain the true nature of the transaction between you and your father regarding the money he took to buy the land. Was it a loan, an agency, or a gift? Because his mere promise to register it in your name is not sufficient for a ruling. The partnership money between you remains as it is, and it is not permissible for you to take anything from it without your father's permission, due to the saying of the Prophet, peace and blessings be upon him: "Indeed, Allah says: I am the third of two partners, as long as one does not betray the other. If he betrays him, I depart from between them." You can inquire from him or refer to a scholar.