Crack egg shells and peel carefully. Sometimes peeling under cool running water can be helpful. Be sure not to break the egg white. Once eggs are peeled, cut in half lengthwise and remove egg yolk placing them in a small mixing bowl. Add egg whites to a plate or serving platter.
Add mayo to egg yolks and combine. Add 1 tablespoon of diced red onion and 1 tablespoon of capers to yolk mixture and fold in.
Once combined, scoop yolk mixture into the 12 egg whites. Garnish with remaining diced onion and capers. Sprinkle Everything But the Bagel seasoning over the deviled eggs and serve.