So you want to use a fork of any existing vendor extension with your Yii 2 install and use the fork, instead of original source. This does not need you to push any update or register your package on packagist.org. You are recommended to follow the approach below:
The tips here are for advanced usages of composer and its assumed you have read about using composer and have a knowledge of your vendor packages to be updated. Let's consider, you want to update only one specific yii2 vendor library, without updating all the other extension packages?
Ok, you have installed a Yii 2 basic or advanced app for the first time and completed the post install steps. You have picked up a few extensions to install for the first time as well. You would already see a composer.lock file in your application root folder.