What is a eagle quarter?

Do you mean "eagle quarter" or "quarter eagle"?

There really isn't any US coin called an "eagle quarter"because ALL quarters up to 1998 had an eagle on the back.

However, there WAS a coin called a "quarter eagle" - it was a gold coin with the somewhat strange denomination of $2.50 that was issued up till the US went off the gold standard in the early 1930s.