Preheat the oven to 350°F (175°C). Grease a 9x13-inch baking dish with cooking spray or butter.
In a large skillet over medium heat, melt 1 tablespoon of butter. Add the chopped onion and sauté until translucent, about 3-4 minutes.
Add the sliced yellow squash and zucchini to the skillet. Cook for an additional 5-7 minutes, stirring occasionally, until the vegetables are tender. Remove from heat.
In a large bowl, combine the corn, sautéed vegetables, shredded cheddar cheese, milk, eggs, salt, black pepper, garlic powder, and paprika. Mix well until all ingredients are evenly combined.
Pour the mixture into the prepared baking dish. In a small bowl, combine the breadcrumbs with the remaining melted butter, then sprinkle the breadcrumb mixture evenly over the top of the casserole.
Bake in the preheated oven for 30-35 minutes, or until the casserole is set and the top is golden brown. Let it cool for 5 minutes before serving.