If my spur theory is correct, there is a small portion of the larger spur piece still attached and you should be able to see a square outline when looking at the back end of the serpent where it attached to the spur.
It's likely part of a civil war officer's spurs. I did a little research online and the design is similar to Brigadier General James J. Archer's spurs that were sold on an online auction not too long ago.