It would help if you used the tutorials fuzzy posted to upload an image, so we can help you figure out exactly what you have. However, it does sound like you are describing a repunched mintmark.
Here's a link to a list of the known repunched mintmarks for 1960 pennies: http://www.varietyvista.com/02b%20L...20(1-60).htm
Also, the value of a repunched mintmark varies greatly depending on the grade or condition of the coin. We need pictures to figure that out.





















