The victim has been identified as 10-year-old Pritam Kumar.
His father Jagat Narayan Mehta and his brother Gautam Kumar (6) have been admitted to a private hospital in Banmankhi sub-division in a serious condition, Banmankhi Sub-divisional Police Officer (SDPO) Kundan Kumar said.
The incident occurred near Ram Nagar Parsahi panchayat on NH 107 under Janki Nagar police station when Jagat Narayan Mehta was going to attend a family function at Gokulpur village after picking up his two children from the school on motorcyle, Kumar said.
An FIR has been lodged with the concerned police station on the basis of statement made by the victim's father, the officer added.