public class MySpecialDimensionEffects extends DimensionSpecialEffects
{
        public MySpecialDimensionEffects()
		{
			// These are the same parameters that Overworld uses, do whatever you like here
            super(192.0F, true, DimensionSpecialEffects.SkyType.NORMAL, false, false);
        }
		
		// We're required to implement these two following abstract functions
		
		@Override
        public Vec3 getBrightnessDependentFogColor(Vec3 biomeFogColor, float daylight) 
		{
            return biomeFogColor; // Implement this however you like
        }

		@Override
        public boolean isFoggyAt(int x, int y)
		{
            return false; // Implement this however you like
        }
		
		// Here is where the important part starts, the renderSky() function runs during the step when LevelRenderer renders sky.
		// If you override this function, whatever you code here will execute every frame.
		// The return of this function specifies whether you want to render the Vanilla sky as well (false) or if you want to cancel the rendering of the Vanilla sky (true).
		
		// !!! Works pre-1.21 !!!
		@Override
		public boolean renderSky(ClientLevel level, int ticks, float partialTick, PoseStack poseStack, Camera camera, Matrix4f projectionMatrix, boolean isFoggy, Runnable setupFog)
		{
			// Here you can render whatever you like, assuming you know how rendering works, which is a totally different beast from just making a custom sky for a dimension.
			// You can check out LevelRenderer from Vanilla for inspiration.
			
			return true; // By default this function returns false, but if you want to get rid of the Dimension's original sky completely, make this method return true
		}
		
		// !!! Works post 1.21 !!!
		@Override
		public boolean renderSky(ClientLevel level, int ticks, float partialTick, Matrix4f modelViewMatrix, Camera camera, Matrix4f projectionMatrix, boolean isFoggy, Runnable setupFog)
		{
			// Here you can render whatever you like, assuming you know how rendering works, which is a totally different beast from just making a custom sky for a dimension.
			// You can check out LevelRenderer from Vanilla for inspiration.
			
			return true; // By default this function returns false, but if you want to get rid of the Dimension's original sky completely, make this method return true
		}
    }
}

public static final ResourceLocation EFFECTS_ID = new ResourceLocation(mymodid, "custom_effects"); // You can just create a new ResourceLocation instance directly in the register() method if you won't be using it for anything else

...

@SubscribeEvent
public static void registerDimensionEffects(RegisterDimensionSpecialEffectsEvent event)
{
	event.register(EFFECTS_ID, new MySpecialDimensionEffects());
}