Rajeev Singh was shifted to a hospital and is battling for life, the official said.
The accused, Ajeet Singh, was arrested and a case was registered against him.
"Singh had fired at his son in a fit of rage while they were having an argument over some family issue, at their residence in Dagani village," the official said.
"The weapon of offence and an empty cartridge has been seized from the scene," he said.