Lazarus

Doctor McCoy notifies Kirk that the fallen man is awake and Kirk questions him. Kirk learns that the man, who calls himself Lazarus, is chasing down the "monster" who destroyed his civilization. He describes his nemesis as a murdering beast, existing only to destroy.

Lazarus frequently fades in and out of existence, encountering his adversary in a kind of dimensional corridor. Each time he does so, another energy wink occurs that ripples through the universe.

Kirk takes Lazarus to the bridge when Spock reports an amazing discovery on the planet: a "rip" in space and time has formed near where Lazarus was found. Lazarus insists that his enemy, trying to destroy the universe, is causing the phenomenon. He demands that Kirk give him some dilithium crystals so he may fix his ship and continue to fight his enemy. Kirk refuses, so Lazarus steals some dilithium from the ship's engines. Once Lazarus is caught, Kirk takes him to the briefing room for interrogation. Lazarus denies doing it, saying his enemy must have stolen it.

Kirk beams back to the planet with Lazarus and a security team to seek this "hidden" enemy. Lazarus has another dimensional episode and is returned to sickbay, where Kirk demands the truth. Lazarus explains that he is a time traveler, and the planet below was once his homeworld. He claims his counterpart destroyed his civilization in the past, for which Lazarus chased him for centuries.

Spock concludes that Lazarus's enemy is an "anti-Lazarus", possibly from a parallel dimension; if Lazarus and his anti-self contact each other within either physical universe, they would destroy each other and annihilate both universes.

Lazarus, prepared to continue his mission, slips away from sickbay and creates a diversion in engineering to acquire dilithium. With the stolen crystals, he beams down to the planet to repair his ship. Kirk follows, but Lazarus activates his time machine just as Kirk tries to stop him. Stepping into the portal, Kirk is accidentally teleported to the other anti-dimension where he encounters the anti-Lazarus.

This Lazarus seems sane and admits to stealing the dilithium the first time. He informs Kirk that his people believed two universes existed, tried to prove it but failed, thus causing their own destruction. Lazarus confirms Mr. Spock's hypothesis that breaking the barriers between the matter and anti-matter universes may trigger doomsday.

He explains that only one Lazarus can exist in a universe at a time and his opposite went mad to the point of seeking the double's destruction, even if that meant the end of the world. If not stopped, their constant encounters will destroy both universes. The anti-Lazarus tells Kirk that the "dimensional corridor" — Lazarus's ship — connecting them must be severed. Kirk must send the mad Lazarus back into the corridor and close off the portal for good.

Kirk returns to his universe and confronts the insane Lazarus, pushing him into his dimensional portal. Kirk heads back to the Enterprise, ordering the phasers to target the dimension ship. The two Lazaruses meet once more and fight as phaser beams vaporize the ship. Both Lazaruses are now trapped between universes, apparently doomed to fight each other for eternity.

https://en.wikipedia.org/wiki/The_Alternative_Factor