"Quadrennially" Natural Recordings by Native Speakers
Every four years.
The word "quadratura" is an Italian term with Latin roots. It generally means "square shape" or "squareness" in English. In art and architecture, it can also refer to a painting technique that involves creating the illusion of three-dimensional space on a flat surface.
I couldn't find any word in English that matches the spelling "quadrel". However, I think you may be referring to the word "quadrille", which is a noun that refers to a type of ballroom dance or a set of four playing cards.