[jQuery] Cross server check if a pdf file exists

[switch13]

I'm trying to see if a pdf file exists in a directory on another
server. If it does, do one thing, if not do another.

Here's what I tried:
                $.ajax({
                        url: url,
                        type: 'GET',
                        dataType: 'jsonp',
                        jsonp:'jsonp_callback',
                        error: function () {
                                
$('.Row').eq(i).children('td:eq(2)').append(file_unavail);
                        },
                        success: function(){
                                
$('.Row').eq(i).children('td:eq(2)').append(file_avail);
                        }
                });

I can get it to work on the same server by removing the dataType and
jsonp but I was search around and read that the jsonp would allow me
to get around the Access to restricted URI denied" code: "1012

I'm I doing something wrong? Is it possible to do what I'm asking with
jQuery?