Does Naruto Uzumaki belong to a special clan?

Nope. But they have not shown any history of uzumaki clan. Till now Naruto is only the one from his clan.

Update: Yes, he is from the Uzumaki clan that has been mentioned and talked about by Kushina (his mother) in the manga, Ch. 500. The Uzumaki clan specializes in seals and were attacked and destroyed during or after the war.

Update: in naruto chapter 510 uchiha madara reveals that nagato is from the uzamaki clan