In a large bowl, combine diced corned beef, drained sauerkraut, shredded Swiss cheese, cream cheese, and Dijon mustard. Mix thoroughly, cover, and refrigerate for 30 minutes.

Scoop a tablespoon of the filling and roll into a 1-inch ball. Place on a lined baking sheet and refrigerate for an additional 15 minutes.

Set up a breading station with shallow bowls of flour, beaten eggs, and breadcrumbs.

Roll each ball in flour, dip in eggs, and coat in breadcrumbs.

Heat vegetable oil in a skillet or deep fryer to 350°F. Fry the balls in small batches for 2-3 minutes until golden brown.

In a medium bowl, whisk together mayonnaise, ketchup, pickle relish, hot sauce, and smoked paprika until smooth to make the dipping sauce.

Serve the crispy Reuben Balls hot with the dipping sauce.