Alternative forms 
- tinker's dam
However, this is just polish added to an old phrase, as not worth a damn predates the use of tinker's damn. The reference to tinkers was added for emphasis and colour - tinkers were known for swearing, so a damn from a tinker was particularly worthless. Also, it was a way, as with "Fudge" or "Geez Louise" or a million other soft-core curses, to avoid saying the actual word "damn" while pronouncing the word "dam."
- tinker's cuss (mostly British)