Galaxy S3 Mini screen seems to get touched when there's no actual touch
My opinion is the screen might be grounded with some metallic or conductive object inside the phone. Probably a loosened part due to use. You can try to wave a strong magnet (like neodymium) at the back of the phone. Data shouldn't be affected anyway because flash chips are resistant to magnetism. But its still much better if you can get it repaired thru warranty.