1976 Tehran incident: a large mysterious craft is spotted above the city of Tehran, Iran. The military dispatches two fighter jets to intercept the object. The first one has a system failure and has to turn back. The second one continues and eventually gets close enough to spot it, it is a rather large craft. He panics and arms his missiles and as he is about to fire all his weapons systems stop functioning. Then an object shoots out of the craft and comes right at him, he assumes it is a missile and tries to take evasive measures. Moment before the object is about to hit him it suddenly dips under the craft, circles back around it, and heads back to the larger craft. Needless to say the pilot flies away in a hurry.
You can find this story using the FOIA. So we have a craft that not only performs aerial maneuvers that no aircrafts we have could possibly do, but is also somehow able to selectively shut off the systems of a fighter jet, since everything but his weapons continued working just fine.