The correct option is A Adjective Clause
A clause is a part of a larger sentence containing a subject and a predicate of its own.
A Principal Clause is an independent clause which can exist even without a subordinate clause. A Subordinate Clause is called a dependent clause because it cannot exist without the help of the principal clause. It begins with a subordinating conjunction.
In this sentence, 'The house belongs to my father' is the principal clause and 'that I live in' is the subordinate clause.
The subordinate clause qualifies the subject 'the house' in the principal clause, thereby acting as an adjective. Hence, it becomes a subordinate adjective clause.
So, Option A becomes correct and the other three options cancel out.