What is the origin of the word “shot” with regards to the drinking term “Give me a shot.”

Solution 1:

(Adapted from my answer on the original Skeptics question)

The word "Shot", a corruption of the Late Old-Engish "Scot" or "Secot", itself a corruption of the old Norse "skot", was a word meaning a Tax or measure.

A serving of spirits was originally, and unimaginatively, a measure, for which "shot" was a synonym that moved into common parlance. (Also, much later, a "jigger")