The party has fielded a senior leader, E Madhusudanan, who has held the seat before and has influence among Telugu people who have a sizeable presence in RK Nagar.
The campaigning ended on Tuesday amid allegations of bribery and circulation of unverified videos of notes distribution. The Election Commission has refused to postpone the by-poll further despite pleas from the opposition DMK. But the Election Commission said there was no proof.
The by-election was postponed in April this year over allegations that the faction of jailed AIADMK leader VK Sasikala paid Rs 89 crore to voters to buy support for its candidate and her nephew TTV Dhinakaran.
The AIADMK is up against TTV Dhinakaran, and the DMK's Marudhu Ganesh, a little-known lawyer but an RK Nagar local who is seen by many as the frontrunner for the seat in today's by-election.
Mr Dhinakaran was evicted along with his aunt VK Sasikala as a result of the AIADMK's two factions led by Mr Palaniswami and former CM O Panneerselvam merging in August this year. Mr Dhinakaran and Sasikala have challenged that decision and claim to lead the real AIADMK, though their support in the party is dwindling.
The video was released by V Vetrivel, a legislator of the AIADMK who is now in the Mr Dhinakaran camp.
The AIADMK has repeatedly raised questions about Ms Jayalalithaa's hospital stay and death, implying that Sasikala and her family hid the true picture for political reasons and were responsible for the situation leading to her death.
Mr Dhinakaran had said that he did have video proof of Ms Jayalalithaa alive and recovering in hospital, but did not want to show it to the world as the former Chief Minister would not have liked to be seen in that state.
While the BJP has fielded a candidate too, the Left parties and the MDMK are supporting the DMK, which wants to win RK Nagar to deliver a big psychological blow to the AIADMK and support its claim that the ruling party has lost popular support after the death of Ms Jayalalithaa only months after she led her party to a big win in the assembly elections last year.