You can add custom javascript by creating a custom/custom.js in the UberMenu plugin directory.  There is a custom-sample.js file which you can rename to custom.js get started.
To automatically enqueue this script, go to the UberMenu Control Panel > General Settings > Assets and enable Load Custom Javascript

Note that, depending on your script, you may need to disable UberMenu’s Remove JS Conflicts setting in the UberMenu Control Panel > General > Script Configuration
