People of Khilparha and Sadhurkhil clashed in a local market around 8pm on Wednesday, said Chatkhil Police Station OC Aminul Islam.
He, however, could not confirm whether anybody was injured.
Saddam Hossain and Abdur Rahim, hit by bullets, were admitted to a local private hospital.
Witnesses said a group of young people of Sadhurkhil clashed with those of Khilparha in the market over a trivial matter.
They fired eight rounds and vandalised four shops and two pickup vans.
OC Islam said additional police has been sent to the troubled area.