Had a quick look at the link you sent me and it seems like there is a issue with jQuery. You are going to have problems adding jQuery to the index.html page in the adapt build folder as adapt does not load jQuery like a normal web page.

Ideally I would not alter the index.html file and would instead build an adapt extension to add the menu functionality. There is some information on this on the GitHub wiki (https://github.com/adaptlearning/adapt_framework/wiki/plugins), we are planning to add some guides to developing themes, plugins and extensions.

There is an example of a menu on the following post: 

https://community.adaptlearning.org/mod/forum/discuss.php?d=222