Superintendent of police control, Uttam Bhaumick told PTI that the residents of Gournga Tilla lynched the three after they were spotted trying to crossover to Bangladesh with a cow from the village at around 4.30 AM.
The village is about 45 kms from here.
The three had entered the country from Chunarughat upazila of Habibganj in Bangladesh.
Bhaumick said a police case was registered and investigation was on.
State police and BSF personnel have rushed to the spot and a flag meeting is likely to be held with the Border Guards of Bangladesh (BGB) for handing over the bodies, BSF sources said.