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tinker's dam[sic]

Technically, "dam" is correct as it relates to a tool of a tinker. However either "dam" or "damn" is acceptable as noted below:

What is A Tinker’s Dam?

Definition: Something completely worthless. (As is this debate. Take it to another board.)

Origin of a Tinker’s Dam
There is some disagreement regarding the spelling of this idiom. Some claim it is tinker’s dam while others say it should be tinker’s damn. To understand this, it is important to know that a tinker is a person who travels from one place to another repairing small things like utensils.

An early definition of tinker’s dam, recorded in the year 1877, stated that a tinker’s dam was a piece of doughy material that tinkers would use to hold metal in place when repairing it. The idea was that this material was worthless once the repair was complete, since it couldn’t be reused and could serve no alternative purpose.

However, other early versions of this idiom include a tinker’s curse and a tinker’s cuss. Apparently, back when being a tinker was still a common profession, there was a stereotype that tinkers cursed often. This is similar to the modern stereotype about sailors. If a tinker cursed often, then the severity or importance of each curse would be small. Damn, then and now, is a common curse.

https://writingexplained.org/idiom-dictionary/a-tinkers-dam