Most often high school students do research in a university under a professor. Has there been any instances where a student published a paper in a peer-reviewed journal without any help from a professor?
It's unlikely but not impossible.
To use an example, I once had a colleague reviewing a paper where a high school student produced some results from a commonly used mathematical model in epidemiology. While not duplicative, they weren't exactly novel. Yes, no one had published for this model and this disease in this population, but these results were very much of a "Yes...and?" variety.
But the journal in question was pushing the "Papers should be technically correct, and excitement or novelty is less important."
I don't know the final outcome of that paper, but it's conceivable that it could have been published.