Eight more were injured in the fighting over the shallow water body at Kulonj Union at noon on Tuesday, said Dirai police OC Abdul Jalil.
The deceased are Tajul Islam, 32, Shaharul Islam, 25 and Ujjal Miah, 35.
The injured have been taken to Sylhet Osmani Medical College and Hospital.
Locals Ekrar Hossain and Masuk Chowdhury were in a long dispute over occupation of the Jalia Jalmahal, said OC Abdul.
The clash intensified when the rivals went to fish at the Jalmahal at dawn. Tajul Islam died on spot during the hour-long clash.
The fighting stopped after police arrived at the scene and took ten injured men to the hospital.
The three dead men have bullet wounds on their bodies, said Brig Gen Abdus Sabur Miah, director of the Sylhet Osmani Medical College and Hospital.
Shaharul died on the way to the hospital and Ujjal died during treatment, he told bdnews24.com.
Police have been deployed to prevent further clashing in the area, according to Dirai police.