1) The boy who arrived here Tuesday was running late.
Explanation:
A clause is a group of words with a subject and a verb that may express a complete thought on its own (independent clauses) or that may not (dependent clauses). Clauses acting as modifiers to subjects, or other nouns are called "adjective clauses."
Sentence number 1 is the correct sentence because the adjective clause "who arrived here Tuesday" modifies or provides further information to the noun "the boy", which it's also the subject because it is the one that performs the main action "of running.