In a large mixing bowl, combine finely chopped corned beef, sauerkraut, Swiss cheese, cream cheese, and Dijon mustard. Mix until evenly blended.

Cover with plastic wrap and refrigerate for 30 minutes.

Scoop 1-inch portions and roll into balls. Refrigerate for 15 minutes.

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

Roll each ball in flour, dip in eggs, then roll in breadcrumbs.

Heat vegetable oil in a skillet to 350°F (175°C).

Fry the balls for 2-3 minutes until golden brown, turning occasionally.

Drain on paper towels to absorb excess oil.

Whisk together mayonnaise, ketchup, pickle relish, hot sauce, and smoked paprika until smooth.

Arrange the Reuben Balls on a platter and serve with dipping sauce.