Automate publish post with markdown & GIT

Hi, I’m looking for a way to automatically publish posts that I push to a private git repository that I have on my server.

The idea is to edit my markdown files locally and when the remote repository is pushed, the posts will be published automatically. This is interesting when it comes to correcting errors and having the files updated on both sides (local and remote).

For example, I edit an article in local and I send it to my remote repository, then it is automatically published. But I realize that there is an error in the text, then I edit it in local and send another push to the remote repository, automatically updating the post.

Can you think of a way to do it?

For now, I have only found the way to import markdown files but in case of correcting errors, you would have to upload the file again, edit the tags, etc, etc …

thanks!