1. Informal. wrong end foremost; completely backward: an arsy-varsy way of doing things.
1. Informal. in a backward or thoroughly mixed-up fashion: The papers are all filed arsy-varsy.
Lucas left her to press Lestrade, who was awkwardly composing a narrative in which he was a marginal figure, brought in arsy-varsy. He found the old guide waiting impatiently, in fear that his clientele would evaporate amid disorder.
— Robert Stone , Damascus Gate , 1998…
a gob, a prayer, a lesson, a little of each, a prayer got by rote in case of emergency before the soul resigns and bubbling up all arsy-varsy in the old mouth bereft of words, in the old head done with listening, there I am old, it doesn’t take long…
— Samuel Beckett , Stories and Texts for Nothing , 1967
This term first came to English in the 1530s. It is probably an alteration of the Latin vice versa with arse substituted to make a facetious rhyming compound.