How to fork a repository and run off your own code

To fork a repo and run your own code and fixes instead, do this in composer.json

{
    "repositories": [
        {
            "type": "vcs",
            "url": "https://github.com/igorw/monolog"
        }
    ],
    "require": {
        "monolog/monolog": "dev-bugfix"
    }
}
lang-json

Note, this is taken from the official documentation:
https://getcomposer.org/doc/05-repositories.md#vcs

The explanation on this Stack is:

Note that you don't change the require statement except to specify your bugfix branch. You still reference the upstream package (monolog/monolog), not your personal fork (igorw/monolog), and the branch name is prefixed with dev-.