“S’mores” is the correct spelling. Probably a playful contraction of “I want some more”.
It looks well documented.
https://en.wikipedia.org/wiki/S%27more
The text indicates that the treat was already popular with both Boy Scouts and Girl Scouts. In 1927, a recipe for "Some More" was published in Tramping and Trailing with the Girl Scouts.[5]This could almost be a bit from Mr. Peabody's Wayback Machine.The contracted term "s'mores" appears in conjunction with the recipe in a 1938 publication aimed at summer camps.[4] A 1956 recipe uses the name "S'Mores", and lists the ingredients as "a sandwich of two graham crackers, toasted marshmallow and 1⁄2 chocolate bar". A 1957 Betty Crocker cookbook contains a similar recipe under the name of "s'mores".