The accused, identified as Satyandra, has been arrested and sacked, Superintendent of Police Om Prakash said.
The constable was posted as guard at the answer sheet collection centre of the UP Board of High School and Intermediate Education within the college campus, he said.
When some employees of GIC accused him of being drunk on duty and threatened to lodge a complaint, Satyandra allegedly fired in which Nagendra was killed, the SP said.
Another person, Hariom (37), an employee of Sakoti Inter School was injured and admitted to a nearby hospital, he said.
A case has been registered, Om Prakash said.