The 'Permission denied (publickey)' error appears when GitHub’s SSH authentication cannot verify your identity, often due to a missing or unlinked SSH key. Start by generating a new SSH key if you haven’t done so already (`ssh-keygen -t rsa -b 4096 -C '[email protected]'`) and add the generated public key to your GitHub account under *Settings > SSH and GPG keys*. Use `ssh-add ~/.ssh/id_rsa` to add your private key to the SSH agent. Next, test your SSH connection with `ssh -T [email protected]` to confirm that authentication works. If you receive a successful message, retry your push. If you’re still encountering issues, ensure that your SSH config file (`~/.ssh/config`) has entries for GitHub, specifying the correct IdentityFile and Host details. This configuration enables seamless, permission-granted access for future operations.