By Mohammed Mukhashaf and Sami Aboudi ADEN, March 29 (Reuters) - Yemeni fighters loyal to the Saudi-backed President Abd-Rabbu Mansour Hadi clashed with Iranian-allied Houthi fighters on Sunday in downtown Aden, the absent leader's last major foothold in the country. Hadi loyalists in the southern port city reported a gun battle in the central Crater district in which three people were killed, and said they recaptured the airport, which has changed hands several times in the last five days of fighting.