The mother-son duo have been identified as Anju Devi (37) and Prashant (16). Anju's husband, Raman Chaudhary, who has a computer repair shop nearby, was not at home when the alleged incident took place, police said.
Locals told police they heard Anju screaming in the afternoon that somebody was attacking her son with a knife.
But when locals surrounded the house, the accused locked himself inside, police said.
While Anju was declared dead at the hospital, Prashant is believed to have died on the spot, police said.
The accused, who is as yet unidentified, is currently admitted in hospital where his condition is said to be critical, they added.
A case of murder has been registered in connection with the incident, police said.