> on-premise

I think the correct term here would be "on-premises".

A premise and a premises are not related concepts except in the sense that the "premise" of this comment is to let you know that "premises" is the correct term to use.

I'll also accept "on-prem" because it could reasonably be a shortened form of "on-premises" (even though most people probably don't realize this and are instead reinforcing their misconception when they use it).