the main Archive of Our Own tag for 'The Little Vampire' (the original German 'Der kleine Vampir' books, I assume, not the later movie?) is pretty sparse, but there's a tiny, dedicated pocket of it. I found one writer on AO3 who does these super thoughtful short pieces focusing on Tony and Rüdiger's friendship, less on the spooky stuff and more on the loneliness and connection from the books. FF.net has maybe a dozen stories total, mostly older and some are... not great, a bit juvenile. Your real luck might be in German fan spaces, if you're willing to dig or use translation. I remember stumbling on a forum years back with some surprisingly mature takes on the characters, but I lost the link.
For English stuff, filtering by 'book fandom' not 'movie fandom' on AO3 helps narrow it. Don't expect a huge treasure trove; it's more like finding a few well-kept secret notes someone left in a library book. The quiet nature of the fandom means the writers who are there tend to be really passionate about the original tone, which I appreciate.