Nazia Husain, her husband and 16-year-old son have been accused of killing of Vinay Mahto, who studied in Class 6 of Sapphire International School with Nazia's daughter.
"Vinay was killed because of his affair with the teacher's daughter," said police officer Kuldeep Dwivedi.
The daughter has also been detained for her alleged role in trying to hide the crime.
On Friday, 12-year-old Vinay was invited for a midnight meal by Nazia Husain's teen son, who allegedly told him that his sister would be present.
Vinay was seen on CCTV footage walking at around 1 am towards the hostel near the edge of the school campus, in which his teacher and her family stay. A little later, Vinay was found unconscious on the steps of the hostel.
The police say when Vinay arrived at the teacher's home, her son demanded that he end his friendship with his sister. When Vinay reportedly refused, the teen started beating him and allegedly bashed his head against the wall.
According to the police, the commotion woke the teacher and her daughter, who were sleeping in the next room. On seeing Vinay lying in blood, they allegedly panicked.
They allegedly dragged Vinay out of their home and pushed him off the first floor. Then they went on to clean up the blood stains.
A badly wounded Vinay was spotted by another teacher who was returning to his quarters after late night preparations for the school annual function.
The boy died later in hospital.
After questioning at least seven schoolteachers, a forensic team reportedly found bloodstains from Nazia Husain's home. She broke down and confessed during her interrogation, the police say.
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