This drink belongs to the "tini" trend and is one of the first of this era. Here is an early printing of this drink:
Complete world bartender guide - Page 60 by Bob Sennett in 1993 "Apple Martini - 1 part vodka 1 part DeKuyper Sour Apple Pucker Pour all ingredients into a shaker. Shake well and strain into a martini glass."
Dekuyper themselves do not claim to know when Apple Pucker was introduced, however, Apple Barrel Schnapps was introduced in 1996. It is likely this was drink was originally printed on the back label of a bottle of Apple Pucker, although, we do not know when that was. This drink has as a definative origin, but as mentioned above, the date is unclear.
There is also a confusion of composition, As early as 1997 Apple Martinis or Appletinis began to consist of "Sweet & Sour" Mix, to sweeten this overly powerful taste of pure spirits. It is undetermined why this is, our best guess would be a magazine or newspaper printed sweet and sour as an ingredient in this drink. Although, there is no literature supporting this, it is only speculatory.
This drink dates between 1987 - 1991 and contained at least as of then:
Stir these ingredients:
Apple Pucker (DeKuyper)
If you are going to use the modern recipe, shake all the ingredients