No, the Earth has gravity just because it has mass. It would have almost exactly the same gravity even if it wasn't spinning at all. As the distance from the surface of the increase, the force of gravity decreases because the gravitational forces universally proportional to the square of the distance.
Instead of asking such questions, it would be a good idea to learn classical mechanics. These lectures, https://www.feynmanlectures.caltech.edu/ would be a good place to start.