The Viper Mark III is the third iteration of the Viper space superiority fighter. It was developed and first put into service during the First Cylon War. Seeing action during the First Cylon War, the Mark IIIs were presumably intended to replace the older Mark IIs; it is implied that this never fully happened for some reason, as the Mark IIs are still shown as being in use during the final battle of the First Cylon War.
The fighter has presumably since been superseded by the newer Viper Mark VII; none are seen during the Fall of the Colonies, meaning that all fighters of its type were likely retired and presumably either scrapped or refurbished for display.
Its first (and only) appearance in the RDM universe has been in the Battlestar Galactica: Blood and Chrome miniseries.