Sauté the shrimp: Melt the butter in a skillet over medium heat. Add the shrimp, garlic, paprika, salt, and black pepper. Cook just until the shrimp turn pink and tender, then remove from heat.
Chop and fold: Roughly chop the cooked shrimp into small pieces. Mix with cream cheese, mozzarella cheese, and half of the chives until the filling is creamy and evenly combined.
Form the rolls: Place a portion of shrimp cheese filling near the lower edge of each egg roll wrapper. Fold in the sides, roll tightly, and seal the edge so the cheese stays tucked inside.
Crisp the wrappers: Fry the shrimp rolls in oil at 350°F for 3 to 4 minutes per side, until deeply golden and crispy. For baking, bake until crisp and browned.
Finish with chives: Let the rolls rest briefly so the creamy shrimp filling settles. Scatter the remaining chives over the warm rolls.
Serve warm: Serve with ranch or garlic dipping sauce while the wrappers are crisp and the cheese center is melty.