The three were admitted to a local hospital where they succumbed to burn injuries, police said.
25-year-old Seema, a slum dweller of Maldahiya area of the district, set herself and her 4-year-old son and 2-year-old daughter afire by pouring kerosene, police said.
The woman took the extreme step following an altercation with her mother-in-law Sudama, who was also injured in the incident.