Most likely your local repository is still configured to use a HTTPS URL to access the GitHub repository. You need to change the URL to the SSH one. You can find the right URL by clicking the green “Code” button on the repository page and selecting “SSH”, it should look something like this:
You can change the remote URL with the following command (change URL and remote name as needed):
git remote set-url origin email@example.com:user/repo.git
origin is the default remote name for where you initially cloned from. If you need to use something different, you probably already know.
See also: Git - Working with Remotes