Happy Singh, aged 16, and Dharm Prakash Yadav, also of the same age, were locked in a verbal duel over a dispute, they said.
This happened during a cricket match in Dubha area, police said.
Happy Singh went to his house, brought a country-made fire-arm and allegedly shot at Yadav, they said.
Yadav was first rushed to the district hospital and later referred to Varanasi, police said.
Happy was absconding after the incident, they said.