The incident took place this morning when Anita Pandey (26) set herself and her children Rishabh (4) and Trishna (2) afire after pouring kerosene oil, they said.
While the children died on the spot, Anita was rushed to hospital, where she died during treatment, Superintendent of Police Manoj Kumar Jha said.
Anita's husband also got injured while trying to save her.
Police is probing the matter.