The incident occurred on Saturday night when some people were returning from a marriage function and their vehicle hit the car of Annu Paswan, who is the brother of the ruling SP MLA from Balrampur Sadar, Jagram Paswan.
Police said both the sides got into a heated exchange of words and in a fit of rage Annu allegedly fired at Jairam Yadav (40), who died on the spot.
An FIR has been registered against Annu, Pappu and Angad.
Police have seized the vehicle and are trying to apprehend the accused who are absconding, Superintendent of Police Pradeep Kumar Yadav said.
Meanwhile, demanding immediate arrest of the accused and compensation for victim's family, locals blocked the Lucknow-Gonda highway.
However, police reached the spot soon and pacified the protesters.