Purpose is to get content from both public and private repositories. In addition to that looking for a scheduled syncing process to update the content in my endpoint when the git Hub wiki updates (As a further enhancement).
https://github.com/user/project.wiki.git tried this but it does not fit to my purpose
GitHub wikis are git-backed and as far as I know there is no REST API alternative.
This was the original blog announcement: https://github.blog/2010-08-12-making-github-more-open-git-backed-wikis/
So I think the git interface at https://github.com/user/project.wiki.git, as you mentioned, is the only option.