The Cthulhu Mythos, created by H.P. Lovecraft, has inspired a wide array of fanfiction across various platforms, including Archive of Our Own (AO3) and FanFiction.net.

https://www.fanfiction.net/book/Cthulhu-Mythos/

https://archiveofourown.org/tags/Cthulhu Mythos - Fandom/works

Cthulhu Mythos Crossovers - https://www.fanfiction.net/crossovers/Cthulhu-Mythos/5763/

Batman Vs Cthulhu - https://forums.giantitp.com/archive/index.php/t-331740.html

Similar plot expanded in the comics Batman: City of Madness by Christian Ward

More link in this post from Red : https://www.reddit.com/r/FanFiction/comments/ots4fo/i_want_to_read_more_cthulhu_mythos_crossover/

And, as one of the best Mythos/Sherlock crossover ever, let’s not forget - A Study in Emerald by Neil Gaiman, winner of the the Hugo, Bram Stoker, Locus, World Fantasy, Nebula Award.

Here the comics version by Rafael Albuquerque

Honorable mention