There is no known story with this title. We only learn the following from a letter (#133) that Howard wrote to Tevis Clyde Smith, circa June 1930:
Well, me bauld buccarearo, since writing the above I stopped and wrote a ten page story, “The Fangs of the Copperhead” which I intend to try to sell Fiction House. It took me about three hours to write it, but I bet I don’t sell it.
Completely unrelated, Howard writes about snakes in a letter (#152) to Lovecraft and mentions copperheads:
In the east part of this town the country is sandy and copperheads used to abound. A few years ago a big snake of that species bit a child, striking her with such force that he knocked her down, and then biting her repeatedly while she was on the ground.