Add water. Pour 1 cup of water into the Instant Pot insert and place the trivet inside.
Add eggs. Arrange the eggs in a single layer on the trivet.
Pressure cook. Lock the lid, set the valve to Sealing, and cook on high pressure for 5 minutes.
Release and chill. Do a quick release, then immediately transfer the eggs to an ice-water bath and chill for at least 5 minutes.
Prep the yolks. Peel the eggs and slice them in half lengthwise. Scoop the yolks into a bowl and mash well with a fork.
Make the filling. Add the mayonnaise, mustard, relish, salt, and pepper. Stir until smooth and creamy.
Pipe. Transfer the filling to a piping bag and pipe it into the egg-white halves.
Garnish. Dust with paprika and top each with a slice of sweet gherkin. Chill until ready to serve.
Serve and enjoy!