When I feed my bream, I have 2 catfish that come up for the food. The larger of the two is seen the most and he's a bluish silvery color. Channel cat? Blue cat?

The last thing I need is a pond full of catfish.
Any idea how to get rid of them?

Catch em and release in the grease. Or use a small hook and a little worm , set the cork just an inch or so above the hook and then feed the fish ,set line out.... You might catch a perch or two but you will catch them

Pat W

Probably came with the fish you bought and planted.

Yup, I'm agreeing with Cecil. Likely hitchhikers, if it was more than 2 I'd be more concerned.