Preheat oven to 350°F (175°C) and grease a 9x13 inch baking dish.
Slice yellow squash into 1/4-inch rounds. Remove any large seeds if your squash are mature.
In a large skillet over medium heat, melt 2 tablespoons of butter. Add the squash and diced onions. Season with a pinch of salt to help release moisture.
Cook for 8-10 minutes, stirring occasionally, until the vegetables are just tender but not mushy.
Transfer the cooked squash mixture to a colander and gently press with a spoon to release excess liquid. Allow to drain for at least 5 minutes.
In a large mixing bowl, combine the cream of chicken soup, sour cream, beaten eggs, garlic powder, paprika, cayenne, salt, and black pepper. Whisk until smooth and uniform.
Fold the drained squash and onion mixture into the creamy base. Add 3/4 cup of the grated cheddar cheese, reserving the rest for topping.
Pour everything into the prepared baking dish, spreading evenly with a spatula.
In a small bowl, combine the crushed Ritz crackers with the 2 tablespoons of melted butter.
Sprinkle the remaining 1/4 cup of cheese over the casserole, then distribute the buttered cracker mixture evenly across the top.
Bake for 35-40 minutes, until the topping is golden brown and the casserole is bubbling around the edges.
Allow to rest for 10 minutes before serving to let the flavors meld and the casserole to set properly.