A community dedicated to fediverse news and discussion.
Fediverse is a portmanteau of "federation" and "universe".
Getting started on Fediverse;
WriteFreely would be your best bet of what exists. However, the communities are small between instances, and there's not any search algorithm or anything to my knowledge.
With what currently exists on the Fediverse, I think that having a WriteFreely and posting what you write to: your own Lemmy community; a Mastodon account; a Pixelfed account; depending on your needs and use, would be the best way of going about it within the current ecosystem as it exists.
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No federated alternative as of yet. It's one of the platform types that the fediverse is lacking.
Dreamwidth (which is not a platform to host fanfiction, but rather to discuss it, share recs, etc) has had federation proposals, but nothing has come out of them.
WriteFreely is in the fediverse, but it's more of a blog platform the style of blogger, wordpress, or medium.