When My Baby Comes To Town was recorded by the Modern Mountaineers in 1940
Moon Mullican, piano/vocal; Johnny Thames, banjo; Aubrey “Red” Greenlaw, guitar; Bill Mounce, bass
https://m.youtube.com/watch?v=CutFVRQGFHk

I can’t find a definitive attribution, but it’s likely the song was composed by Moon Mullican
https://en.m.wikipedia.org/wiki/Moon_Mullican

Thanks for posting your chart

)BOB