I don't believe there's any connection between Adams and Alaska, aside from the fact that both designs are the work of Medallic Art Company. The Adams obverse is from its popular presidential series; I have the Whitman Bookshelf album produced in the early 1960s to house those medals.

The Adams medal has a plain border, while the Alaska medal has a beaded border, and that tells me that this is most likely a mule - whether an authorized muling or a clandestine product is anyone's guess. I'll be interested to read what Dick Johnson has to say about it.

Your recent request for information linking John Adams to Alaska piqued my interest and, having the Adams Family Papers staff literally down the hall, I forwarded it to them. They are an amazing group of researchers and editors and I knew that if there were a reasonable answer, they'd find it.

So here it is: if you go online to Google Scholar and locate the Boston Alaskan, vol. 1 August 1906-June 1907, edited by L.M. Norton (Boston-Alaskan Society: Boston, 1907) on page 11 you can find a quotation by John Adams that Senator Charles Sumner used during his speech to advocate the acquisition of Alaska…

"Thirteen governments founded on the natural authority of the people alone, without a pretense of miracle or mystery, and which are destined to spread over the northern part of that whole quarter of the globe, are a great point gained in favor of the rights of mankind." John Adams, "Defense of American Constitutions," January 1, 1787. [my italics, AEB]

Sounds reasonable to me. Thanks Adams Papers staff!