I want to check if a file exists locally, where the HTML file is located. It has to be JavaScript. JavaScript will never be disabled. jQuery is not good but can do.
Since 'Kranu' helpfully advises 'The only interaction with the filesystem is with loading js files . . .', that suggests doing so with error checking would at least tell you if the file does not exist - which may be sufficient for your purposes?
From a local machine, you can check whether a file does not exist by attempting to load it as an external script then checking for an error. For example:
File exists?
Some notes...