Election Commission sources said polling was proceeding peacefully, and there were no reports of violence.
Over 7.34 lakh voters are eligible to express their choice in 81 polling stations to choose their representatives from among 18 candidates, including three women, in Kaliaganj, Karimpur and Kharagpur Sadar.
In Kharagpur Sadar's booth number 140, the BJP agent complained that the Electronic Voting Machine was strategically placed beside a mirror wall.
"Because of the mirror wall, it could be seen who the people are voting for. So we have complained," said the agent.
The mirror wall was later covered with a paper by the election authorities.
In Karimpur, BJP alleged that its agent in Thanarpara was kidnapped allegedly by Trinamool Congress workers. The Trinamool denied the allegations.
The BJP candidate Jay Prakash Majumdar met with resistance from some people, alleged to be Trinamool loyalists, when he went to the booth. The BJP contestant got involved in heated verbal exchanges with them, till the central force personnel intervened and removed the people.
Majumdar was asked to leave a booth at Pipulkhola school after allegations from Trinamool that he was going too close to the EVM.
On the other hand, Trinamool candidate Bimalendu Sinha Roy was found to have entered a booth with the party symbol displayed on his dress. He was ordered out of the booth.
The ruling Trinamool Congress and the opposition BJP are contesting all the seats.
The Left Front and Congress have formed an alliance with the Congress in fray from Kharagpur and Kaliaganj and Left Front major CPI-M in Karimpur.
The polls at Kharagpur Sadar and Karimpur were necessitated after the MLAs Dilip Ghosh and Mahua Moitra won the Lok Sabha polls.
The bypoll in Kaliaganj is the fallout of the death of Congress MLA Pramath Nath Roy.
Though the bye-elections are not going to bring about any change of government, they have generated much interest among political observers and analysts, who feel the results and voting trends could give a fair idea, and even to some extent, shape the future course of events in the run up to the 2021 Assembly elections.
( With inputs from IANS )