It's not possible to save content to the website using only client-side scripting such as JavaScript and jQuery, but by submitting the data in an AJAX POST request you could perform the other half very easily on the server-side.
However, I would not recommend having raw content such as scripts so easily writeable to your hosting as this could easily be exploited. If you want to learn more about AJAX POST requests, you can read the jQuery API page:
http://api.jquery.com/jQuery.post/
And here are some things you ought to be aware of if you still want to save raw script files on your hosting. You have to be very careful with security if you are handling files like this!
File uploading (most of this applies if sending plain text too if javascript can choose the name of the file) http://www.developershome.com/wap/wapUpload/wap_upload.asp?page=security https://www.owasp.org/index.php/Unrestricted_File_Upload