It is recommended to use TypeScript for SPFx development. If you want to use existing JavaScript file you can do a simple hack, rename your custom.js file to custom.ts file. The functionality that you want to be available from this file should be exported. consider below JS code in your custom.js
var customMessage = "Hello JS string";
export default customMessage;
Here we are exporting customMessage. You can assign JS function as well and export it from this file.
Going back to your MyDocumentsWebparts.ts file, add import for this file:
import customMessage from './Assets/JS/custom';
I can just display this string value:
<p class="ms-font-l ms-fontColor-white">${customMessage}</p>

now you have access to exposed functionality using customMessage variable! Build process will make sure that this import file content is included in output. This is beauty of SPFx build process -;