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Since Y was J in German and ea was ä, the original name may have been Jägli. The Jägli family may have originated in Germany or Switzerland. If you search Swiss databases, you will find numerous references to the name Jägli, especially around Zurich. The references name a Jägli as a mayor of a city, a Captain of Knights (next to king in military power), and even one who was probably in the Crusades. The Swiss references go back to the 1200s. As I understand it, the "Jäg" part refers to a warrior, or a knight. You can still find Jäglis in Switzerland, today.
The names Yeagley, Yeakel, and Yeagle (as well as Yeakle), are very definitely related--they most likely come from the same root.
I come from the Yeagley's in Berks, Lebanon, and Lancaster counties in Pennsylvania. Although most of my relatives stayed in Lebanon County, it appears that some moved to Ohio and perhaps then on to Indiana, etc.