"Neither Trinamool nor CPI(M) stopped infiltration of Bangladeshis to India as it is part of their agenda for creating votebank," he said at a public meeting here.
He said the party wants fencing along the porous Indo-Bangladesh border to stop infiltration.
"If the BJP forms its government here, not even one Bangladeshi, can enter India (illegally). That is why we had a border agreement with Bangladesh. We want fencing in the border so that there is no infiltration," he said.
"When elections are going on at the same time in the same country in two different places, you have an alliance in one state and in another, they are fighting each other. Is it the fight of principle or for getting chair?" Shah said.
BJP candidate Chandra Bose, a descendant of Netaji Subhas Chandra Bose, is pitted against Mamata Banerjee from the Bhowanipore assembly seat in south Kolkata.
Questioning Banerjee over the sale of her paintings, he claimed that her high-priced paintings were bought by those involved in the Saradha scam.
On the recent collapse of Vivekananda Road flyover in the city that killed 27 persons, he said the Trinamool government could have cancelled the contract for building if as they said they were "unhappy" with the project.
"The flyover didn't fall down due to wind. It collapsed because of the syndicate. All materials - cement, iron, etc are supplied by Trinamool. The flyover is a symbol of corruption," he alleged.
Referring to the Narada sting operation, Shah said he had never seen anyone taking money so shamelessly.