Just Anti-Social Counterparts
Originally started out as the Anti-Freedom Fighters, a rebellious group of bikers. The casually bashed heads with their other selves, the Freedom Fighters.
They were the ones who overthrow their version of King Acorn instead of Robotnik.
As the Freedom Fighters look for Sonic as their champion, the Suppression Squad loathe the Anti-Sonic so much that they kicked him of the group.
After the Anti Sonic became Scourge and return back to his world with Fiona Fox, he decided to some 're-vamping' of his home by re-naming it Moebius, have everyone to take a different name or changing their names, and declaring himself King!
All the members of the Squad except for Fiona, fear Scourge because of his power. So they secretly plot againist him by having Miles, Tails' counterpart, make a truce with the Freedom FIghters. After an major battle, the Squad managed to send Scourge back to Moebius, with Sonic too.