The two arrested men have been accused of slapping a police officer who was on duty during the incident.
Investigators are examining CCTV footage from the area to reconstruct the sequence of events and identify others involved in the confrontation.
Of the four FIRs registered at Kalighat police station, two were filed by the police over alleged assaults on their personnel. One of these complaints explicitly names Abhishek Banerjee.
The other two cases stem from rival political complaints. One FIR was registered against unidentified BJP workers following a complaint by Banerjee, while a counter-complaint by BJP workers named the TMC leader and several others.
What happened at Abhishek Banerjee's residence?
According to police, clashes erupted between Trinamool workers gathered to celebrate Banerjee's 39th birthday and BJP supporters between 2 am and 3.30 am on Saturday.
Former West Bengal Chief Minister Mamata Banerjee and Abhishek Banerjee subsequently staged a protest, alleging that his Kalighat residence had been attacked.
Abhishek Banerjee alleged that a group he described as "BJP goons" had targeted his residence and office after conducting reconnaissance for two days.
The TMC MP has not yet issued a statement on the incident.
Separate police case over Banerjee's convoy
In a separate development, Kolkata Police have also booked Abhishek Banerjee under provisions of the Bharatiya Nyaya Sanhita (BNS) and the Motor Vehicles Act following a complaint by Rajiv Sarkar, a resident of Baguiati.
Sarkar alleged that Banerjee's convoy routinely violated road safety regulations, claiming that security personnel drove dangerously while other guards hung precariously from the exterior of the moving vehicle.
Police also pointed out that Banerjee's security personnel have frequently been seen standing on the outer footrests of his vehicle while it is in motion.
In his complaint, Sarkar cited Section 123 of the Motor Vehicles Act, which prohibits drivers and passengers from travelling while holding on to the outside of a moving vehicle. He also invoked Section 184, which deals with dangerous driving.
Other legal challenges facing the TMC MP
The latest police cases add to a series of legal challenges involving the Diamond Harbour MP.
Abhishek Banerjee is being investigated by the Enforcement Directorate (ED) and the Central Bureau of Investigation (CBI) in connection with alleged corruption cases.
He has also faced scrutiny in an ongoing signature mismatch investigation.
Separately, the Madhya Pradesh High Court recently withdrew interim protection granted to him in a defamation case filed by Akash Vijayvargiya, son of BJP leader Kailash Vijayvargiya.
His 'Sebashray' outreach programme in the Diamond Harbour constituency has also faced allegations of corruption.
The latest developments have intensified the political confrontation between the Trinamool Congress and the BJP in West Bengal, with competing complaints now forming part of the police investigation.