Two persons were injured in a shootout in the city's Tiljala area on Saturday morning, a senior police officer said.
The injured were identified as Raju Roy, a taxi driver, and his father, Dablu Roy.
They were admitted to the Calcutta National Medical College and Hospital, the police officer said.
The incident took place in Tarikhana Road when a few locals, who had asked for money from Raju, allegedly surrounded him when he was returning home with his brother, and an altercation followed, the police said.
"Soon one of them pulled out a gun and fired a couple of rounds, injuring Raju and his father, who had come there to pacify them," he said.
The miscreants then fled while hurling country-made bombs, the officer said.
An investigation has been initiated.
A huge police team was deployed at the spot where the incident happened, he added.