The BJP and its student organisation - ABVP was on one side, with the Congress party and the CPI-M and its student wing on the other.
Trouble broke out at the Kerala Varma College, Thrissur, when student activists of the ABVP were beaten up by the activists of the Student Federation of India (SFI) activists - of the CPI-M.
The difference of opinion was simmering in the college for a few days now as the ABVP wanted to organise a seminar on CAA and SFI was opposed to it.
It was decided that when things cool down, this can be discussed later.
But on Wednesday, according to the local police, trouble broke out and the students belonging to the rival organisations clashed with each other and it was only after the staff members of the college intervened, things cooled down.
"So far no case has been registered," said a police official on condition of anonymity.
The college principal was not reachable, while other officials of the college agreed that there were skirmishes between students and now things have cooled down.
Likewise at the Palakkad Municipality - the only one ruled by the BJP in Kerala, the day's council meeting turned for the worse when skirmishes broke out between the ruling BJP councillors and the opposition - Congress and the CPI-M.
Speaking to , Bhavadas, a Congress councillor said right from start of the council meeting, it was tensed.
"The CPI-M came out with a resolution and demanded that it be taken up for discussion and it pertained to the passage of the CAA - which we also felt was one which will divide the country and hence wanted this to be discussed at the meeting. With the ruling BJP-led NDA unwilling to take it up, tempers ran high and it ended with a free for all as councillors came to blows," said Bhavadas.
In Kerala, both the ruling Left and the Congress-led opposition have been strongly opposing the CAA and they organised a joint protest, here on Monday with Chief Minister Pinarayi Vijayan, his cabinet colleagues and Leader of opposition Ramesh Chennithala and other UDF leaders sat together to send a message that this will not pass muster in Kerala.
The BJP has just one legislator in the 140 member Kerala Assembly.
( With inputs from IANS )