my great aunt fanny

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 1, 2013