Combine minced garlic, olive oil, hot sauce (if using), smoked paprika, citrus zest, citrus juice, salt, and pepper in a bowl to create the marinade.
Add the shrimp to the marinade, ensuring they are fully coated. Let them sit for at least 10 minutes so the flavors can penetrate the shell, and the shrimp start to turn pink.
Preheat your grill to high heat and brush the grates lightly with oil to prevent sticking.
Place the marinated shrimp shell-side down on the hot grill. Sear for about 2-3 minutes until you see grill marks and the shells begin to turn slightly charred.
Flip the shrimp carefully using tongs and cook for another 2-3 minutes until the shells are crispy and the shrimp are opaque and tender.
Brush the cooked shrimp with a little more olive oil for added shine and flavor, then remove them from the grill.
Serve the shrimp hot, shell-side up, with lemon or lime wedges for extra brightness and a smoky, spicy bite.