Is it permissible to borrow with interest to build a house for one's children, given that the father has given his son a plot of land for this purpose, and he must vacate his apartment for his brother within a year?

It is not permissible to take interest-bearing loans to build an apartment because borrowing with interest is forbidden by the Book, the Sunnah (definition), and the consensus of scholars. It is not permissible except in cases of dire necessity that cannot be dispensed with, and building an apartment is not among necessities. If you cannot build on the land through permissible means, then explain the matter to your father and abandon the land if necessary, for whoever gives up something for the sake of Allah, Allah will compensate him with something better.