It's not really known whether Mojoverse is an alternate reality or a different dimension. It is said that the Mojoverse and it's inhabitants is unique to the Multiverse, so there's supposedly no alternate versions of Longshot and Mojo.
The Mojoverse was created by Ann Nocenti and Art Adams and first appeared in Longshot Vol.1 issue 1 (1985).
Major Story Arcs
A Brief History
The universe is inhabited by races that watch television all day long. Mojo is the ruler of this reality/dimension and is the only producer that decides what will air on television and what will not. But in more recent times, a resistance to Mojo's rule has begun, most prominent players have been Longshot and (for some time) Dazzler and Shatterstar.
Due to Longshot's ties to the X-Men, the mutantgroup has had their fair share of trips and fights towards and in the Mojoverse. More recently, even Howard the Duck was revealed to have his own show in the Mojoverse.
Earth 1610 (Ultimate Universe)
In the Ultimate Universe there exists counterparts of Mojo and Longshot. These counterparts originates from Earth and are human, so it could be argued that they are not really counterparts, just happens to share the same name, and in Longshot's case the same powers.