Yes, there are quite a few interesting Joker and Batman 'brothers' fanfictions out there. Some explore the idea of an alternate universe where they are raised as brothers, which completely changes their dynamic. It's fascinating to see how the Joker's chaos and Batman's order could be reimagined within a family context.
In the comics, Joker and Batman are not half brothers. Their connection is based on their ongoing conflict and opposing natures rather than any blood relation. The dynamic between them is what drives the story forward.