Please see my answer re 'fool' above as regards this idea you have about "invention". The 'e' version you are asking about now is just one of the many spelling variations that existed in past times. Here are some of them...scitte, schit, schyt, scheitt, scheitte.
To help with any future such questions, try to bear in mind that 5/600 years ago, spelling in English was far from standardised...different writers just spelt things as seemed best to them. Some of these caught on and some didn't...simple as that. Nobody ever sat down and thought, "I know! I'll stick an extra letter on here and see what happens!"