jgit provides a ListNotes command which can provide either specific or all notes in the repository. From there you can then read the not-content.
You can see an example of how this is used at the jgit-cookbook in the Snippet ListNotes.java.
The actual data can then be fetched by a normal Blob-read because notes are stored as normal blobs like file contents, i.e.
ObjectLoader loader = repository.open(note.getData());
loader.copyTo(System.out);