What is the most convincing evidence for the existence for a supernatural being?
The most convincing evidence for the existence of God, at least for me, is the indirect evidence provided by the inspiration for the Bible (and all the evidence which supports belief in the inspiration of the Bible). For this I strongly suggest you get a copy of my book Reasons for Belief (www.ipibooks.com)
However, I believe that is not really the kind of "evidence" you have in mind. I assume you mean evidence from outside of Christianity. In that case, my answer is that nature itself–with its obvious beauty, complexity, order and so forth is the greatest evidence for God. This is what Paul seems to be saying in Romans 1:18-23. He says that the existence of God is obvious "from what was created." As a scientist, the more I delve into the laws of nature and the unbelievable complexity of even the simplest life and the "fine tuning" of the parameters which define the universe, I find that the impact of this evidence becomes much stronger. I have a LOT on this topic in my book Is There a God? (www.ipibooks.com). The way Isaac Newton put it: "From whence did all the order and beauty arise that we see in nature?" This was a rhetorical question, whose answer, according to Newton, was obvious. It comes from the Creator.