I think the correct sentence is 네 떡 내 먹었더냐 (= Did I eat your cake?). It has a negative meaning. I think this one is rather old style.
하여 놓고 = 하다 + 놓다
체 = pretending
07/12/23
(일) 오후 8:34
hi, i dropped in your blog. i'm a korean and 28 yrs old.
but i've never seen or heard that proverb since i was born.
it is not a proverb.
i think it's a........ some expression in a novel.
good luck for your learning korean!