What is the origin of the contraction では→じゃ? I googled around for a bit, but I wasn't able to find any answer at all.
The contraction is simply a matter of fast speech and sound shapes. で or
/de/ is a front-of-the-mouth sound, where affrication is not uncommon. Consider how English don't you often becomes doncha in fast speech, or how could you becomes cudja. So too with では --
/de wa/ →