Github does not allow the creation of private forks for public repositories.

The correct way of creating a private fork by duplicating the repo

1. Create a bare clone of the repository. (This is temporary and will be removed so just do it wherever.)

   git clone --bare https:/github.com/user/repo-name.git

2. [Create a new private repository on Github name it repo-name.

3. Mirror-push your bare clone to your new repo-name repository.

   Replace <your_username> with your actual Github username in the url below.

   cd repo-name.git
   git push --mirror [email protected]:<your_username>/repo-name.git

4. Remove the temporary local repository you created in step 1.

   cd ..
   rm -rf repo-name.git

5. You can now clone your repo-name repository on your machine (in my case in the code folder).

   cd ~/code
   git clone [email protected]:<your_username>/repo-name.git

6. If you want, add the original repo as remote to fetch (potential) future changes. Make sure you also disable push on the remote (as you are not allowed to push to it anyway).

   git remote add upstream https:/github.com/user/repo-name.git
   git remote set-url --push upstream DISABLE

   You can list all your remotes with git remote -v. You should see:

   origin	[email protected]:<your_username>/repo-name.git (fetch)
   origin	[email protected]:<your_username>/repo-name.git (push)
   upstream	https:/github.com/user/repo-name.git (fetch)
   upstream	DISABLE (push)
   

   When you push, do so on origin with git push origin.

   When you want to pull changes from upstream you can just fetch the remote and rebase on top of your work.

     git fetch upstream
     git rebase upstream/master

   And solve the conflicts if any