Militiamen at a checkpoint in the southern Abyan province stopped the suspected jihadists, prompting an argument that sparked a gun battle, the sources said.
Three Al-Qaeda suspects and the same number of loyalists were killed.
Among the dead was the head of a court set up by Al-Qaeda in the southeastern city of Mukalla, which has been under their control since April, the sources said.
Yemen has been rocked since March by deadly fighting between pro-government forces and Iran-backed rebels, who seized the capital in September 2014 before expanding south.
Aden, Yemen's temporary capital, has been the scene of growing unrest as Al-Qaeda in the Arabian Peninsula, long active in the country, and the newly emerged Islamic State group appear to be vying for influence in the port city.
The extremists are occupying government buildings and are frequently seen patrolling several districts of Aden.
They have carried out several deadly attacks, assassinated government officials and intimidated civilians.
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