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Mutoscope March 1896 Little Egypt. This was a film made for the peephole viewer and marketed by The Magic Introduction Company featuring the New York vaudeville actress/stripper Katherine Devine (sometimes known as Ashea Wabe). Three more films were made or remade in 1897 of the same dancer now for projection in 35mm. She was also involved in a scandal after dancing nude at a stag party hence the denial by Sol Bloom, who had been responsible for the original Streets of Cairo show at the Chicago Exposition of 1893, that she had anything to do with his show. He confuses her however with the dancer at the Streets of Cairo show at Coney Island (1896) who was not Devine.

Edison Fatima's Coochee-Coochee Dance (directed James H. White, filmed William Heise) probably made around the same time (copyrighted 3 May) and originally for the Kinetoscope. This, as far as I am aware, is the ONLY one of the US films of which a copy or copies (censored and uncensored) exists.

The French version of Wikipedia gives an 1893 date and cites Charles Musser's History of the American Cinema but Musser himself is clearly just following Killiam and uses almost exactly the same words. Musser and other researchers claim that other similar uncatalogued films were made for the Kinetoscope and offered privately but only one such is actually cited (by Ray Phillips) - the Dolorita "Passion Dance". Since this was clearly a belly-dance for which Mexicans are not generally known and since the letter that mentions this dates from 6 May 1896 it seems likely that this is in fact just the same "Fatima" film under another name.

The film had a long shelf-life (reviewed in 1899, censored in Chicago as late as 1907) so was evidently transferred for projection in the course of 1896-1897. This starred Fatima Djemille who was performing in The Streets of Cairo show in Coney Island (1896) and was part of a whole series of Edison films shot by White and Heise at Coney Island. There is no reason to suppose (as Killiam, and presumably Musser, both do and as I was inclined to do until Sepiatone produced all the evidence about Coney Island) that it has anything to do with the original 1893 Streets of Cairo show. Sol Bloom also denied in effect that the dancer at Coney Island had anything to do with his show but here he is not on very firm ground. There is ample evidence that Bloom had no idea what happened to the various girls (the show ran round the clock so cannot have involved only one girl) who had performed in 1893. Four of them (apparently named Stella, Zorra, Ferida and Fatima) performed at the Grand Central Palace shortly after the Chicago show closed - and there was possibly a fifth called Zelika - and they were all promptly arrested by the police. So it seems highly probable that Fatima Djemille, performing at Coney Island and for Edison and Mutoscope (1896-1899), was indeed one of the dancers from the original 1893 show. Some accounts suggest that there were two dancers at the Coney Island Show one called Little Egypt and an assistant called Fatima but many of these accounts of Coney Island are heavily fictionalized and this sounds like an invented story.

I had assumed (wrongly) in my imdb review that the 1897 Fatima film was also Edison but, as you pointed out, it is fact a Mutoscope film. Mutoscope actually made another three (Fatima Star of the Orient along with Queen of the Harem and Dance in a Turkish Harem in March 1899). There is nothing surprising about this. Mutoscope were in this case the ones following Edison by filming at Coney Island. I should imagine that the 1897 film and the three 1899 films were also made at the Coney Island show (which did, to judge from the pictures and their captions, mix Arab and Turkish and even Gypsy all together) and all involve the same dancer, Fatima Djemille.