Spoilers from The Prestige and Kaviyathalaivan.
There are some Indian movies that were inspired by The Prestige movie but it's usually just the "Bale is a twin" twist. Just like how people associate Nolan with "time" while he is more than that, his movie The Prestige is associated with this twist but is more than that: jealousy, ego, guilt, curiosity, showmanship, one-upmanship between two diverse people.
One Indian movie that seems to be the closest to The Prestige is Kaaviya Thalaivan. I have watched this movie at home, in college and now in a shared flat. Every time someone sees me watch the movie, they tend to watch it with me till the end. It's not just that the retention rate is so high but also the rate is high for people watching from any point of the movie - I don't know how to call this metric. This movie is so good that even if you had missed that 'The' in the title or if you haven't heard about the movie 'The Prestige' it may have yielded a completely different meaning but still that fits too.
Inspiration, Copy, or Coincidence
The Prestige released 8 years earlier than Kaaviya Thalaivan. So the possibility exists that Kaaviya Thalaivan may have been inspired from The Prestige the movie; or from The Prestige novel which Nolan adapted into The Prestige the movie; or from the real life story of magicians Houdin and (maybe imaginary) rival; or from the book written by Houdini about Houdin; or considering how time may not linear with Nolan, Nolan might have been inspired from Kaaviya Thalaivan; or maybe Vasanthabalan watched The Prestige, forgot it (like Ghajini which may have been inspired by Memento, also by Nolan) and wrote KT and some elements may have appeared here -- If so then this is technically Inception, by Nolan.
Vasanthabalan’s Veyil already has some parts that feel like Cinema Paradiso. You can watch these both back to back and still feel fresh and not one spoiling another so definitely ‘copy’ is not a suitable term here. There is a long list of possibilities and luckily we aren't the hypothetical judges for the hypothetical case Nolan filed against Vasanthabalan so we don't really have to reach the conclusion.
However, you can believe that it is neither an inspiration nor a copy nor a coincidence — that these two movies are completely irrelevant; maybe.
Starting together from the same place
Both pairs of characters, Prithiviraj-Siddharth and Jackman-Bale work under the same mentor at the start of the movie.
Modern vs Conventional
Prithiviraj and Jackman, the antagonists, are more traditional while Siddharth and Bale, the protagonists are more modern and innovative.
Arc of the mentor
In The Prestige they work for a magician named Milton (reference to this post’s author, or is it?) but he doesn't have much screen space; instead Michael Caine plays the role of their mentor. He and Nassar share similar arcs.
Initially, the mentor supports the newcomer protagonist (Siddharth/Bale), when the antagonist complains. But over the course of time the mentor takes a stand against the protagonist:
Caine testifies in court that Bale is a murderer while Nassar curses Siddharth. Later they return to the original state of understanding and supporting them. This is by itself the flow established in the movie: The Pledge, The Turn and The Prestige.
One loses the lover thanks to the other
Prithiviraj creates chaos preventing Siddharth from reaching his pregrant lover Anaika and she commits suicide. Prithviraj is indirectly responsible for that.
Similarly Bale ties the wrong knot (which I believe is due to miscommunication between twins) and Hugh Jackman loses his wife.
CONNECTION WITH REAL LIFE
Both of the movies are pure drama and could run entirely on a fictional space but yet they have many real life attachments. In Prestige we have this Tesla-Edison and in KT we have the Indian independence movement as a wrapper for the story.
ONE OF THEM END UP SHOOTING ANOTHER
Bale performs a magic trick that involves catching a bullet, but a disguised Jackman shoots Bale with a real bullet instead of a trick bullet. Prithiviraj, as well, shoots Siddharth at the end of KT.
Drunkard actor who unexpectedly performs well
Hugh Jackaman need a body double for his transporter trick so he finds a drunkard. That drunkard is an actor who went out of business long ago. Though a drunkard performs much opposite to everyone's expectation.
In Kavithalaivan, Siddharth will be a drunkard at some point. Prithviraj needs some one actor and he is cornered to take Siddharth. People doubt whether Siddharth can do as he may have forgotten verses but instead he ends up giving a great performance.
Stealing the stage
Hugh's transporter man is designed in such a way that Hugh enters through one door and the above-mentioned alcoholic dupe exits via another. In one play, Bale appears instead of the dupe, and the dupe being held captive on stage indirectly captures the show's The Prestige moment.
Similarly in Karnan drama Prithiviraj is the hero of that but Siddharth who plays Arjunan spins a song on the spot and captures the stage.
Love for the Co-worker
Scarlett Johanson who actually worked as an assistant to Hugh Jackman at some point works for Bale and falls in love with him. We see a similar arc in Kaaviya Thalaivan when Vedhika works as an actress in Prithiviraj's troop but falls in love with Siddharth.
Guilty & Last Speech
Both the movies end with a speech from the antagonists’ perspective, moving the audience with empathy even though they may not be making logical sense.
If you tell the entire The Prestige plot from the POV of the women characters it will be more like Iraivi. The twin brothers killed two women, one with a knot in her hands and another in neck. Scarlett Johnson lost her lover as Hugh Jackman traps and gets him legally executed. Bale's daughter lost her mother. Roughly you could match characters, victims and plot with Iraivi.
The Prestige 2
Hugh Jackman could have had a pair of backups of his clone safely out there and they could return anytime after actual Hugh as Lord Caldlow got killed. Though Bale's Borden identity is dead the Fallon identity is there and with the availability of the clone machine after killing Lord Caldlow they could clone Fallon and start from the beginning. At Least Caldlow doesn't have a name in magic. But Fallon being Borden's assistant is a huge advantage. Now the game starts again with Two Hugh Jackman's, Two Bale's with a time machine and caine on their side. But with many mysteries resolved this won't be The Prestige 2 instead it will be just another Cat and Mouse game.