Preheat the oven to 425°F (220°C).
In a large bowl, combine the baby potatoes, 1 tablespoon olive oil, 1 tablespoon Cajun seasoning, 1/2 teaspoon smoked paprika, 1/2 teaspoon garlic powder, salt, and black pepper. Toss well to coat.
Spread the potatoes on a large sheet pan in a single layer. Roast in the oven for 15 minutes.
Meanwhile, in the same large bowl, combine the shrimp, crab legs, corn, remaining 2 tablespoons olive oil, 1 tablespoon Cajun seasoning, 1/2 teaspoon smoked paprika, 1/2 teaspoon garlic powder. Toss to coat evenly.
Remove the sheet pan from the oven and add the shrimp, crab legs, and corn to the pan, mixing gently with the potatoes.
Return the sheet pan to the oven and roast for an additional 10 minutes, or until the shrimp are pink and cooked through and the potatoes are tender.
While the seafood and vegetables are roasting, mix the melted butter with minced garlic in a small bowl.
Remove the sheet pan from the oven and drizzle the garlic butter evenly over the shrimp, crab, corn, and potatoes.
Sprinkle the chopped fresh parsley over the top and arrange lemon wedges around the pan.
Serve immediately, squeezing lemon juice over the seafood and vegetables as desired.