Place the eggs in a large pot and cover them with cold water. Bring the water to a boil over medium-high heat. Once the water reaches a boil, turn off the heat, cover the pot, and let the eggs sit for 10 to 12 minutes.

Transfer the eggs to a bowl of ice water and let them cool completely. Once cooled, peel the eggs carefully and slice them in half lengthwise. Remove the yolks and place them in a mixing bowl.

Mash the yolks with mayonnaise, Dijon mustard, hot sauce, Cajun seasoning, lemon juice, pickle relish if using, salt, and black pepper. Mix until the filling is smooth and creamy. Taste the filling and adjust the seasoning if needed.

Melt the butter in a skillet over medium heat. Season the shrimp with Cajun seasoning and garlic powder. Add the shrimp to the skillet in a single layer and cook for 1 to 2 minutes per side, or until the shrimp turn pink and are fully cooked.

Add lemon juice to the shrimp and remove the skillet from the heat. Do not let the shrimp sit in the hot pan too long because they can become tough.

Spoon or pipe the yolk filling into the egg white halves. Add one Cajun shrimp on top of each deviled egg, pressing it gently into the filling so it stays in place.

Sprinkle the deviled eggs with smoked paprika and garnish with chopped parsley or green onion. Chill for 20 to 30 minutes before serving, or serve immediately if preferred.