Cut the eggs in half and remove the yolk from the egg whites and place the egg yolk in a medium bowl along with the dijon mustard, mayonnaise, pickle relish, and hot sauce. Season with salt and black pepper. Mash the yolk mixture with a fork until smooth and place into a piping bag or a plastic bag with the corner snipped off. 

Meanwhile, heat about 2 inches of oil in a medium pot over medium heat. Place all-purpose flour in one small mixing bowl, beaten eggs in another small bowl, and panko breadcrumbs in a third.

Dredge the egg whites in the flour, followed by the eggs and finish with the breadcrumbs. Add the eggs to the vegetable oil and fry until golden brown and crispy, draining on paper towels after about 2-3 minutes.

Pipe the yolk mixture onto the fried egg whites and top with paprika as a garnish.