The incident happened in the Amirnagar village on Monday.
According to police reports, the deceased has been identified as Farmaan Qureshi of Class 6. He had a quarrel with his three friends over the purchase of a guava after school hours on Saturday.
The three boys, all 15-years-olds, asked him to buy guavas for them too, but Qureshi refused.
On Monday when Qureshi reached school along with his cousin Tauheed, all three of them attacked him and thrashed him mercilessly.
All the three were caught by the school staff and then handed over to police.
Basic Shiksha Adhikari (BSA) Budhpriya Singh said: "The police have taken necessary steps in this case while we have ordered a probe to ascertain whether any negligence was shown on the part of any school teacher."
An FIR has been registered against the three under IPC section 302 (murder) on the complaint of Qureshi's father and the boy's body has been sent for post-mortem.
Senior Superintendent of Police (SSP) Poonam along with District Magistrate Shailendra Singh rushed to the village and spoke to the aggrieved family.
They also spoke to the main accused boy who had allegedly punched and kicked Qureshi. The boy claimed that he never intended to kill him and had only punched him in the stomach.
Qureshi's father Saimur, however, said: "My nephew Tauheed, who studies in the same school, told me that Qureshi was thrashed by the three school children in the presence of a school teacher. The accused sat on his chest and repeatedly thrashed him to death."
Station House Office (SHO) Sanjay Tyagi said that an FIR has been registered against the three children, but initial investigations indicate that only one of the accused beat up the deceased.
"We have recorded the statement of the school children, who witnessed the fight between the boys and it seems like it was an accidental death. We are waiting for the autopsy report to ascertain the main cause of death. The accused will be sent to juvenile home."
( With inputs from IANS )