You had me concerned for a second, but “mists of time” shows up on Wiktionary (easier to be wrong), Merriam Webster’s site (likely to be right) or the Oxford English Dictionary (practically canonical), whereas “midst(s) of time” does not.
Collins Dictionary and Dictionary.com don’t list either, but the existence of the former in other places would seem to suggest that that’s the right one.





Note for second (or more) language speakers of English (and maybe a few first language folks as well): The plural ‘s’ is omitted when a sentence fragment is turned into an adjective. It’s supposed to have hyphens in it as well, though these are often left out.
So, for example, “My PC is ten years old and runs Linux” becomes “My ten-year-old PC runs Linux”.
In the case of this meme, it should be “My 10-year-old PC”.