There are families with the Atha surname in the U.S. that descended from George Athy/Athey, who was born in Galway, Ireland in 1642 and came to Maryland circa 1662. Some of his descendants changed the name to ATHON, ATHA and ATHANS. My family ended up with it spelled ATHEY.

You might try some of these various spellings. If you know of a male descendant of your great-grandfather, Henry Madison Atha, you should suggest they participate in the Athey DNA study. You can read more about it here: http://www.hprg.com/athey/

Best of luck with your research,
Darlene Athey Hill