There are lots of online literary magazines that specialize in short stories! That's where you learn who the authors in The Genre are, and you can seek out their sites for more.
I know sci-fi/fantasy best, so here are some lit mags I enjoy greatly:
Clarkesworld: probably the most famous and highly respected SFF magazine currently in operation. Mostly (all?) sci-fi.
Strange Horizons: original, weird, often queer. One of my personal favorites.
khōréō: SFF by immigrants, diaspora authors, and works translated from languages originally not in English.
Uncanny Magazine: can lean strange and experimental, but also one of the most respected SFF mags currently in operation.
Lightspeed Magazine: lots of good stuff. Sci-fi focused. Its partner Nightmare Magazine does horror.
The Translunar Traveller's Lounge: specializes in upbeat, fun, or hopeful stories.
FIYAH: Black authors and Black SFF. Not free to read online - you need to buy this one.
Neon Hemlock Press: emphasizes the queer and weird. Has a flash fiction magazine and various books, including short story anthologies.
Apparition Lit: tragically no longer in operation :( but I loved them A Lot and their back issues are still available to read. This one is no longer open for submissions, but all the rest are.
If you want even more indie, there are themed anthology kickstarters running all the time. Input some keywords, sort by "publishing" and "anthology," and see if anything speaks to you.
You can also find out what short stories people liked best by looking at awards lists. The Hugo Awards are sci-fi/fantasy/horror genre awards given every year, and "best short story" (under 7500 words) and "best novelette" (7500-17,500 words) are categories awarded every year. If your preference is "queer stuff," the Lambda Literary Awards name a "best LGBTQ+ Anthology" award every year too. Not only will you find stories there, you'll find authors you can further look up! Some of my absolute favorite short story authors are Darcie Little Badger, Ted Chiang, Isabel J. Kim, N. K. Jemisin, and Julian K. Jarboe.
There are tons out there! This is only the speculative genre publishing world; there are more literary magazines out there I know very little about. But asking people for their favorites is always gonna get you pointed at the the most interesting things!