Route and Execute PHP file (site/custom to run custom.php)

I’d like to duplicate the index.php file, or even the single.php or page.php (or something else) file – rename them, and then be able to access them through a path without modifying the .htaccess file. I figure this shouldn’t be as difficult as I’ve been finding it to implement, but I couldn’t find a suitable answer after much searching around.

Extra points if someone can find out how to link these “custom” paths to the default menu system without requiring hard-coding. ?? But by far, the issue is with what I’ve put up in the first paragraph.

Thanks ahead for looking, hopefully solving this! It just does seem like it should be easy to do.