My parents didn't let us watch much TV when we were kids, so I have seen all of three Twilight Zone episodes. At least I only remember three, but I remember them well, including this one, "Nightmare at 20,000 Feet." It's about a guy who sees a monster on the wing of his airplane, and no one believes him.
I had no idea the man was William Shatner!
I believe the monster is a relative of the Mugatu, who bites Capt. Kirk on Star Trek.
Here's part 1 of 3 (it links to the other 2).