The incident happened at Basanti near Charavidya fair, the police said adding that one of the injured was a policeman.
The deceased were identified as 10-year old Riazul Mollah and 35-year-old Hassan Laskar.
Riazul, a class IV student, was caught in the crossfire when he was returning home from school while Laskar was among those engaged in the fight, the police said.
The policeman was injured while trying to control the situation, a police officer said.
The injured were initially taken to Canning Sub Divisional Hospital from there they were shifted to a hospital in Kolkata, the police officer said.
Nobody was arrested till last reports came in.