Pour buttermilk into a bowl. Place onion slices into buttermilk, cover the bowl with plastic wrap, and refrigerate for 1 hour.

Heat oil in a deep-fryer or large saucepan to 400 degrees F (200 degrees C).

Whisk flour, cornmeal, salt, black pepper, cayenne pepper, and paprika together in a bowl. Working in batches, remove onions from buttermilk, letting any excess liquid drip off, place onions in flour mixture and toss to coat. Shake any excess flour mixture off onions.

Cook onion rings in the preheated oil until golden brown, 3 to 4 minutes. Transfer rings with a slotted spoon to a paper towel-lined plate to drain.