Preheat your oven to 350°F (175°C). Lightly grease a 9-inch baking dish or a medium-sized oven-safe skillet with non-stick cooking spray to ensure easy serving later.
In a large mixing bowl, combine the softened cream cheese and sour cream. Use a spatula or hand mixer to blend them until the mixture is smooth and free of large lumps. Stir in the garlic powder and smoked paprika.
Add the shredded chicken, drained corn, diced green chiles, and half of the shredded cheddar and Monterey Jack cheeses to the bowl. Stir everything together until the chicken and corn are evenly coated in the creamy base. Season with salt and pepper as needed.
Spread the mixture evenly into your prepared baking dish. Sprinkle the remaining shredded cheese over the top. Place the dish in the oven and bake for 20 to 25 minutes, or until the cheese is melted and bubbling around the edges.
Carefully remove the dish from the oven. Let it sit for a few minutes to set, then sprinkle the sliced green onions over the top for a fresh pop of color and flavor. Serve warm.