The incident happened when Amjad Sheikh (45) was coming out of Manikchowk's SBI branch after withdrawing the amount, they said.
The culprit, on a bike, came from behind and tried to snatch Amjad's bag, police said, adding that when he resisted the culprit shoot Amjad and escaped with the bag.
Amjad was rushed to the Malda Medical College hospital and was stated critical, they said.