Bring a large pot of salted water to a boil and cook gemelli pasta according to package directions until al dente.
While pasta cooks, set up a dredging station with three bowls: flour in the first, beaten eggs in the second, and a mixture of Panko and 1/2 cup Parmesan in the third.
Season chicken pieces with salt, then coat in flour, dip in egg, and press firmly into the Panko-Parmesan mixture.
Heat vegetable oil in a large skillet over medium-high heat and fry chicken bites in batches until golden brown and internal temperature reaches 165°F (approx. 3-4 minutes per side); set aside on a wire rack.
In a separate saucepan, melt butter over medium heat. Add minced garlic and cook for 1 minute until fragrant.
Stir in heavy cream, Cajun seasoning, and smoked paprika. Bring to a gentle simmer for 5 minutes.
Reduce heat to low and whisk in 1 cup grated Parmesan cheese until the sauce is smooth and thickened.
Drain pasta and immediately toss with the smoky Alfredo sauce.
Divide pasta into bowls and top with the crispy Parmesan chicken bites.