Documentation for java project (markdown)

I have pretty standard java project with standard gradle layout, all sources are stored in git. I want to write documentation in markdown (or similar markup language) and keep all files in project directory (e.g. docs/ folder in the root). Then I want to generate static site or push my sources somewhere to have access to full documentation in html (should be self-hosted solution).

It will be good if I'm able to add simple link to other articles (like I do it in any wiki engine by using [[article]]). And It would be perfect if I've been able to add quick links to javadoc by the same technique as link to articles. And also it would be perfect if it has had built-in search engine.

I've gone through couple of static site generators but I didn't find anything which can satisfy my requirements at least half. Is there something like that? Or I need to code it by myself (I know it won't take to much time)? Maybe there's more common use case for documentation?