Preheat the oven to 400 degrees F (200 degrees C). Lightly grease 24 (1 3/4-inch) muffin cups with nonstick cooking spray.
Place 1 thawed potato nugget in the bottom of each muffin cup and press firmly with your thumb or the back of a teaspoon to form a crust with a well in the center. Bake until crisp and golden, about 20 minutes. Transfer potato cups to a wire rack and let cool slightly.
Meanwhile, place eggs in a saucepan and add enough cold water to cover by 1 inch. Bring to a boil over high heat. Remove from heat, cover, and let stand for 15 minutes. Transfer eggs to an ice bath and cool for 5 minutes. Peel and set aside.
Add mayonnaise, relish, mustard, celery salt, hot sauce, black pepper, and paprika to a food processor and pulse until combined. Add peeled eggs and process until smooth. Transfer deviled egg filling to a piping bag and refrigerate until potato cups are just warm to the touch.
Pipe deviled egg filling evenly into potato cups.
Garnish with chives and a sprinkle of paprika. Recipe developed by Barrett Heald