Could a being with true power over logic not fool me and its turns out maybe I don't exist after all?

Yes.

Let's assume that the law of non-contradiction is included in our concept of logic. Now, your evidence that you exist is that you exist. But if God has power over logic, then the fact that you exist does not necessarily preclude you from failing to exist. This is because the only reason to treat your existence as evidence against your nonexistence is the law of non-contradiction, which God has power over. Therefore, on the assumption of a God that has power over logic, it is possible that you do not exist.

I don't know if this post will get removed, but it was a lot of fun to write.