What is the ruling on a father's action of registering half of the plot of land, which his son bought with his own money, in his own name, for his brother, without the son's consent?

The land you purchased with your money and for which you appointed your father to buy it is exclusively yours, and what you built upon it with your money is also yours. As for what your brother built on the roof of your apartment with your permission, that belongs to him. If the father's intention with the equal division was what has been previously mentioned, then what he wrote is correct. However, if his intention was for your brother to be your partner in the land and the building by co-ownership, then you are not obliged to accept that, and a father does not have the right to dispose of his son's property to give it to others among his siblings.