Indu Devi (30), resident of Chakkadih village, with her son Raman (5) and daughter Tulsi (2) in tow, jumped before Banka-Bhagalpur passenger train, they said.
While the woman and her son died on the spot, her daughter sustained critical injuries. The girl has been admitted to the Sadar hospital for treatment, police said.
Family feud is suspected to be the reason behind her move, police said, adding a probe was on to find out the details of the incident.