This article shows the step to setup composer to install private Github repository.
On Github
1) Go to settings -> Developer Settings -> Personal Access Tokens -> Fine-grained tokens
2) Clicks on the "Generate new token" button.
3) Select an expiry period

4) Select a specific repo.

5) Provide "Contents" read-only access.

6) Generate and copy the token.
On Target Machine
1) Setup composer auth config by using the following command.
php composer.phar config -g github-oauth.github.com <token>