According to Mojo’s own claim, there are no counterparts of him as there is only one Mojoverse in the multiverse. Following that reasoning, there would be also no alternate versions of Longshot. That, however, would mean that every time a Longshot has made an appearance in whatever timeline, it was just the same, incredibly busy person. The X-Men of at least five different timelines (namely the native realities of Exiles members Mimic, Sasquatch, Nocturne, Morph and Sunfire) have met and fought side by side with Longshot. These times would fit in between the many times that Longshot was mindwiped. Then again – Mojo could have been lying.
As seen during the Shattershot crossover, once the Hundred Years War in the Mojoverse came to an end, Shatterstar was nominated as the Wildways’ ruler. While the situation improved for the Biped race, it was now the Spineless Ones who were forced into slavery. 
Arize couldn’t stand the same errors from the past being repeated and eventually convinced Shatterstar’s former teammates of X-Force to knock some sense into him. Indeed, Shatterstar saw the errors of his ways and fought some of his own followers to install a new order – where Bipeds and Spineless Ones were equal, all of them being “Free Men.” An aged version of Longshot proudly observed from the shadows. Following the reasoning mentioned above, this apparently is the one and only Longshot, one century down the road.
In the Ultimate Universe, Longshot was a mutant with luck-based powers and didn’t hail from another dimension. Named Arthur Centino, he lived on Genosha and fought in the resistance to free the nation from the rule of humans. He met a woman named Spiral and the two began a relationship, but things turned sour when he lost interest in her and she began an affair with a married human politician. Longshot discovered them one night and murdered the man in a fit of rage. 
He was convicted of murder and sent to the island of Krakoa where he would be hunted like an animal on live TV. Some of the X-Men got wind of this new barbaric TV show and flew to Genosha to stop it. Learning the truth from Spiral, though, they decided to leave Longshot to his fate. However, at the same time, another group of the X-Men had landed on the island and met up with Longshot. Under the impression that Longshot was innocent, they helped him defeat the show’s producer, Mojo Adams, and escape the island. He ended up in the Savage Land but was soon captured by the Scarlet Witch under orders from General Fury. He was imprisoned in the Triskelion whilst awaiting extradition but he broke out his cell thanks to Magneto. The master of magnetism was locked up in the prison too and had been planning his escape. He had tipped Fury off to Longshot’s whereabouts, as he had wanted the young mutant’s luck power to aid in his escape. The two fled and Longshot was recruited into the Brotherhood. Luck was not on his side though, when he was tortured and killed by the Mystique, along with the rest of the Brotherhood, on Magneto’s orders.