Is people’s (third panel) correct? Yes!
Here’s how to insert apostrophes: Spell the word. The apostrophe goes after the last letter.
In people, the last letter is “e.” So there you have it: people’s.
Easy, isn’t it?
Incidentally, I loathe the phrase “that of” and never use it. Naturalness trumps grammar every time, at least for me. I would have rewritten the first panel like this:
James Joyce is my persona.
I use James Joyce as my persona.
(To learn more about apostrophes, click here.)