Why and how was the apostrophe invented?
First recorded use is 1588. I got this info from a book called "Making a Point" by David Crystal. Reason for use is complicated, but in short it is to show possession - a contraction of "his".
The sub-title of David Crystal's book is "The Pernickety Story of English Punctuation". That says it all, because to understand the evolution of the apostrophe, you need to look at the history of all punctuation marks. David Crystal is a professor of English Language. His books tackle many complicated aspects of the history of English - spelling is another topic.