To 'josh' has meant to tease or banter with someone for about two hundred years and is probably based on the name of the 19th century American humorist, Josh Billings.
The Oxford English Dictionary gives the earliest recorded use of 'joshing' as having appeared in 1891, well after Josh Billings' (Henry Shaw's) writings were well known. However, it does not go as far as to say the verb 'josh' did come directly from his name, which is why I wrote 'probably' earlier; indeed, there is a recorded use of 'jossing' - with the same sense - dated in the 1850s, so the word might well have nothing to do with the name 'Joshua' at all!