Ahaha. Seen this before. I didn't realize this was a proof. But it's not an S mint. Reading up on it now. "This was the first successful attempt of creating a square coin with reeded edge intended for the artist's community." The Squared Quarter was the brainchild of artist Andor Orand (given name Andor Carius). According to the bio on his own website dedicated to the project, Andor, born in 1942, is a German-American artist who lives and works in the Princeton, New Jersey, and New York metropolitan areas. Although he works in multiple mediums—see the Princeton University Art Museum website for a few examples of his digital artwork—Mr. Orand is perhaps most well-known for his Squared Quarter project. According to a 1982 New York Times feature on the Squared Quarter, the idea to create such a piece came to Mr. Orand in 1972. He began working on the project in earnest around 1980, and the satirical “coins” were finally struck in 1982, although they all bear the date 1984. By the end of 1984, the company set up to sell the Squared Quarter—Square Deal Productions, Inc.—was officially dissolved, and in 1988 the dies, lead die trials, and sample pieces of the various versions that were struck (12 items in total) were donated to the Smithsonian, where they are archived in the National Numismatic Collection. Documentation of the donation confirms that 4 examples of the Squared Quarter were donated (one 1/4-oz. version in silver, one 1/2-oz. version in silver, one nickelsilver (cupro-nickel-zinc) version struck using the 1/4-oz. dies, and one brass version, also struck using the 1/4-oz. dies—and none in gold), as well as 4 lead trial pieces of the 1/4-oz. and 1/2-oz. sizes, and 4 disabled dies for the same sizes. Krause’s Unusual World Coins, 5th ed., even lists the Squared Quarter, and gives the following mintage numbers: 300 in cupro-nickel-zinc (nickelsilver); 1,310 1/4-oz. size in .999 silver; 602 1/2-oz. size in .999 silver; 12 0.3056-oz. pieces in .999 gold; 15 in bronze; and an unknown number in brass. The gold, CuNiZn, bronze, and brass pieces extant were presumably all struck using the 1/4-oz. dies, although it is unclear if any non-silver pieces were struck using the 1/2-oz. dies, other than the lead trial pieces confirmed in the deed of gift to the Smithsonian.
PCGS has said they would grade medals, tokens or coins listed in Krause’s 6th Edition of Unusual World Coins. These are listed on page 679 under Medallic Coinage, Square Deal Productions Issues. There are several varieties made from different metals, brass, silver, gold, bronze and copper-nickel-zinc.
Thanks for the tag! I posted it on CoinTalk in the thread linked below: https://www.cointalk.com/threads/squared-quarter-toned-slabbed.388107/ The one in the PCGS link from @baseball21 is the same one I have.