The story published June 5, 1909, in the Syracuse Post-Standard, was called Ozma of Oz, Continued; or The Quest for the Magic Belt. It was written by two boys, Henry Kutz, age ten, and Max Stolz, age nine.
The heading states that the story was begun July 7, 1908, and finished on July 9, 1908, and is dedicated with love to Uncle Joe--who is Rev. Dr. Joseph Stolz of Chicago, who came to Syracuse to visit his relatives on July 9, 1908.
The two boys seem to have written the story "round-robin" style, one boy writing a paragraph, the other boy writing the next, and so on. Each section is signed by the initials of the boy that wrote it.
What is especially fascinating is that the two boys combine Baum's non-Oz fantasies John Dough and the Cherub and Queen Zixi of Ix and place them in the Oz universe before L. Frank Baum united his fantasy novels in The Road to Oz. The article clearly says (twice) that the story was written in summer 1908. The boys are also the first to introduce the wireless telegraph into the Oz universe, well before Baum does so in 1913's The Patchwork Girl of Oz.
Henry Kutz, the elder boy, also introduced a new group of villains called the "Hollywogs," described as "monster green giants with axes." These also seem like a precursor to future Baumian villains, the Growleywogs, again not introduced until 1910's The Emerald City of Oz.
Given that this fan fiction was published in Syracuse, it would seem quite likely someone sent a copy to Baum and that he found the two boys' idea of uniting all his fantasies in one universe a good one and promptly wrote it into the next Oz book. Perhaps, too, the Hollywogs and the wireless telegraphy. There is no way to know for sure, but Baum often talked of using his young fans' ideas.
Max Stolz's last section seems a bit garbled. He has the Oz group go to see King Bird of Noland. This would seem either a typo on the part of the typesetter, who couldn't read the boy's handwriting, or young Mr. Stolz misremembered King Bud's name as King Bird. The author has also turned Princess Fluff (from Queen Zixi of Ix) into Queen Fluff of Ax [sic], now married to King Azma.
This is a fun little story written by two boys who very much loved the Oz books and Baum's non-Oz fantasies. Enjoy the very first Oz fan fiction!