The injured were Badsha Pramanik, 40, Matin Sheikh, 50, and Abdul Awal, 35.
The incident occurred on Thursday evening ahead of the third phase of the Upazila polls scheduled to be held on May 8. Police have arrested three people with local arms in connection of the incident.
According to police, supporters of the incumbent upazila chairman and upazila unit Awami League (AL) General Secretary Shahinuzzaman Shahin, also chairman candidate, were standing in the Kalirmor area of Bhayana in the evening.
A supporter of opponent chairman candidate Abdul Wahab ran over his motorcycle over the feet of one of Shahin's supporters while he was passing through the road, triggering a shuffle over the issue among the supporters of two groups.
Later, the supporters Wahab, Amin Uddin, chairman of Bhayana Union; and Shahin's supporters locked into a clash. Being informed police rushed to the spot but the supporters of Shahin clashed with them.
Sujanagar police station Officer-in-Charge (OC) Jalal Uddin said Shahin's people attacked the police when police went to calm down the clash. When police fired the shotgun to bring the situation under control, one received a bullet in his leg. Three were held in this regard.
Chairman candidate Shahin alleged that supporters of union chairman Amin attacked them and opened fire on his supporters.
He claimed that some of his supporters shot and injured and they were admitted to local hospital.