28-year-old Swati Jain has been booked under sections 302 (murder) and 309 (Attempt to commit suicide) of IPC, they said.
According to police she smothered to death her two children - Tanwi (6) and Tanish (3) - with a pillow at their home in Shastri Nagar area on the night of January 15.
She then inflicted several injuries on herself suspectedly with a sharp blade and later attempted suicide by hanging herself from a ceiling fan. However, as she could not tie the noose properly, she fell down.
The woman was rushed to a nearby hospital where she is battling for life, while the bodies of the children have been sent for autopsy.
Though the exact reason behind the incident was yet to be ascertained, sources said the couple had a quarrel on January 14.