Short answer, no.
Logic and metaphysics are both based on evidence, and faith is the belief in something for which there is no evidence. Or, rather, faith is the evidence of things unseen, the substance of things hoped for. In other words, to believe that something exists beyond science is to reject the need for evidence or logic.
It's like asking for food that cannot be eaten. You'll find people who claim to have evidence or logic, but it will be conjecture or wishful thinking. You'll find examples of discredited evidence, like the idea that steam rising from a dead body on a cold battlefield was evidence of the physical soul escaping to heaven, or pseudoscience about the weight of a body at the moment of death. You might call that supernatural logic in the same way a rotten cheeseburger is inedible food. Once you abandon a rigorous adherence to the scientific method, it's no longer logic or evidence.
Embrace your faith. Proof is for things that don't require faith.