What is a 1959 wheat penny?

Non-existent. Lincoln pennies with a pair of stalks of wheat on the reverse were produced between 1909 and 1958. In 1959, the reverse was changed to an image of the Lincoln Memorial. There is one suspected "mule" 1959 cent with a wheat-ear back, but its authenticity is very much in dispute. Any others that have been found have turned out to be fakes made by combining halves of genuine 1958 and 1959 cents, using the same techniques that create two-headed magician's coins.