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fanny is a euphemism for the buttocks. So the exclamation "My Aunt Fanny!" or "My great Aunt Fanny!" is to say
"My ass!" as something of a perturbed rebuttal or reply
"I think YOU dented my car."

(surprise and denial) "My great Aunt Fanny! I did not!"
by theguywhobrokethebank November 01, 2013
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