I would like to publish a npm package that contains my source as well as distribution files. My Github repository contains src folder which contains JavaScript
When you npm publish, if you don't have an .npmignore file, npm will use your .gitignore file (in your case you excluded the dist folder).
To solve your problem, create a .npmignore file based on your .gitignore file, without ignoring the dist folder.
Soure : https://docs.npmjs.com/misc/developers#keeping-files-out-of-your-package