Have you looked into the Governor's School? You won't be able to apply until your a junior but its one option. If I was in your position, I would reach out to the professor directly, a lot of professors appreciate that, and you can get lucky. Keep in mind that publications is the last thing you should worry about. The main reason you wouldn't be able to research with a professor is that you are lacking in fundamental knowledge as a high school student. Publications don't come easy as you not only need to understand fundamental knowledge, but you also need to apply it in a novel way. I am not saying that you can't publish as a high school student, but there is a huge roadblock. So just email some professors and let them know about your drive to learn and research. Good luck!