It's my understanding that on D-Day 2 German planes flew over the beaches. Also the Fleet/beaches had a fighter cover consisting of P-38s only to provide Identifiable cover to the very nervous defense teams on the ships.
NOTE: this is over the beaches/ships, inland it was another story with a lot of tacticle flying including B-17/B-24 raids on German defensive positions inland!
Only P-38s?? Wasn't the whole point of the invasion stripes on the wings of allied fighters and bombers for easy identification by ground and naval forces?