It's not a question of suppressing it. It's going to be more a question of determining what, on your system, is requesting privilege escalation. It's not normal to have that pop up "quite often" - it should only be occurring when there is a known action being taken that requires administrative permissions.

@georgecm12 I feel like it has something to do with our imaging workflow. I'm new to Jamf as of April so I used a lot of my predecessors workflow for imaging as I was a little cramped for time. I know the issues won't be there next school year from my workflow but wasn't sure if there was something I could do to eliminate the message for now. I know they alway's pop up if I remote into a machine for the first time using the local admin account. They pop up for both the admin account and then the student account will also start to see it.

I agree with @georgecm12 . Recently, we had a few users who had this problem, and it turned out to be an older version of Google Chrome wanting an update.

After authenticating with the admin rights, I saw the white .dmg Google installer flash on the Desktop quickly, then unmount.

I either updated Chrome, or removed it using an App Cleaner to get all the files, then re-installed.