Scuffle started when BJP leader Rahul Sinha entered the stall at the 44th in the event.
A scuffle broke out between anti-CAA protesters and BJP supporters at the Kolkata Book Fair event on Saturday.
The two sides exchanged blows after West Bengal BJP leader Rahul Sinha entered the stall at the 44th International Kolkata Book Fair around 4.30 pm.
A section of Left-backed students surrounded Mr Sinha when he visited the counter, and raised slogans against the new citizenship law and the National Register of Citizens (NRC).
Police confirmed the incident and said a number of protesters were detained. BJP supporters claimed that one of them suffered injuries in the tussle.
"The people have discarded them (the Left parties). We are not fools to allow them to steal the limelight by getting into a fight with them. Our fight is with the TMC," Mr Sinha, who left the venue after the incident, said.