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:
Using a version control system, like Git, is nice. However, when building an extension from scratch and loading it via Composer, it adds a lot of pain in the butt steps. You have to commit your changes, update composer to pull them over, then notice there is an error, fix, commit, update. repeat.. I don't want all my baby steps under Git. Sure, I could edit my commit history, but c'mon. Just let me code! I will put it under version control once I get a baseline created. This guide will show you how to setup your composer.json to load a local directory (everything inside, live). You make a change, save the file, refresh the page, boom.
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.
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?