The incident occurred on Monday when the victim confronted the accused's family and complained about being stalked by the boys, ASP Jagdish Sharma said.
As per the complaint filed by the victim's family, the accused and their mother thrashed the girl and set her afire, he said.
A case was registered against the trio, Sharma said, adding the sons were nabbed today. The mother was also arrested.
The girl who sustained 95 per cent burns in the incident is fighting for life, police added.