Man, that's a tough one because exclusive content is pretty rare in fanfic circles. Most writers want their work to be read, so they cross-post like crazy. I've been deep in the Teen Titans fandom for years, and I've never stumbled across a platform that has Damian/Raven stuff you can't find elsewhere. AO3 is obviously the main hub; the tagging makes it easy to find. FF.net has a decent amount, but it's older and the search is awful. Tumblr might have some shorter pieces or headcanons that feel exclusive, but they're usually snippets, not full stories. The thing is, writers who do create exclusive content often do it for Patreon or Ko-fi, offering early access or bonus chapters to supporters. But even then, they usually post a public version eventually. Your best shot is finding an author you love and seeing if they have a personal blog or a subscription tier where they share drafts.
I remember this one writer who wrote this incredible slow-burn 'Gotham Academy' AU and posted chapters on their Tumblr a week before putting them on AO3. That felt exclusive for a minute. But mostly, the fandom is too decentralized. Discord servers sometimes have little writing challenges or prompt fills that stay in the server, but those are more like community artifacts than published stories. Honestly, I wouldn't hunt for exclusivity. Just dive into the tags on AO3 and sort by kudos or comments. The really good stuff rises to the top, regardless of where it's posted first.