Sanjay Singh, 45, along with the boy, were killed allegedly by one Gyan Singh, who fired 10 rounds from his licensed double barrel gun in a dispute over a pathway construction in their village, Circle Officer (Sakaldiha) Tripurari Pandey said.
Six people sustained bullet injuries in the incident, he said.
The injured were taken to a district hospital from where they were referred to the BHU Trauma Centre, he said.
The accused, along with two more people, have been arrested, Mr Pandey said.
Earlier, to protest against the incident, angry villagers blocked the Varanasi-Kolkata national highway in front of the district hospital, which was later cleared, he said.