If you write something, you are engaged in authorship. If you want a fancy way of asking "Who wrote that letter?" — try, "Who is responsible for the authorship of that letter?" Fancy, indeed!
Authorship can refer to anything, not just the creation of written text; you can have authorship of a new idea, a new cocktail, a new fashion style — anything. And just as doctors practice medicine, or architects architecture, so writers practice authorship; in other words, authorship also means the actual act of authoring or writing.