Hesham,
I think that the "Fairchild 23" is a typo (which is reoccurs in NACA papers on the F.22 for some reason).
There was an F-23, but that was a postwar ag aircraft (a M-62/PT-19 rebuild/conversion with metal wings). D. D. Funk Aviation created one prototype F-23 (Warner Super Scarab?), 11 F-23As (Continental W-670-M), and 3 F-23Bs (Jacobs R-755B). Some F-23As were converted to 'B standard. A few ended up with Ford auto engines. The F-23 design later evolved into the new-built Weatherly.
BTW, the "Fairchild 23" listed as belonging to the Maharaja of Faridkot Trust is actually a F.24W