The incident was reported from Mirza Inayatullapur Patti village in Unchahar area in the district on Saturday.
The deceased have been identified as Pihu (4), Vidhi (6) and Vaishnavi (8).
The father of the girls Naveen Kumar Singh claimed that he had purchased loose snacks, including puffed rice, from the Jamunapur market on Friday evening and all of them had consumed those snacks, following which they took ill and passed away.
The three girls started vomiting and the family took them to the NTPC hospital where doctors declared Vaishnavi dead, while the other two were sent to the district hospital where they succumbed during treatment, police said.
Upon receiving information about the incident, Sub-Divisional Magistrate (SDM) Vinay Kumar Mishra and police officer Shiv Shankar Singh reached the village and took samples of the snacks consumed by the girls.
"The first two girls died on Saturday while the third girl was getting treatment but she also died at night around 12 at the district hospital. The autopsy of the two girls could not ascertain the cause of death. We have sent a medical team to the village to examine other children there," said SDM Vinay Kumar Mishra.
Officials of the Food Department have been taken away for examination, Mishra added.
Further investigation is underway. (ANI)