Essentially, I've some code inside a my theme folder, within the /js/public.js file. Im using Datatables, and according to their example, im using:

jQuery(document).ready(function() {
    jQuery('#certificates-table').dataTable( {
        "bProcessing": true,
        "bServerSide": true,
        "sAjaxSource": "../wp-content/themes/theme1064/includes/_get_certificates.php"
    } );
} );

Essentially, I have hardcoded the place for SAjaxSource, but I have to use get_template_directory_uri() so its dynamic, or something like that similar...

Any idea how to achieve that within the JS file?

        url: "../includes/_get_certificates.php",
        type: "GET",

        success: function(data) {              
        error: function(XMLHttpRequest, textStatus, errorThrown) {
        timeout: function () {

Are you certain your file pathways are correct? If you're creating a Wordpress admin feature, your files might be within the wrong place. The conventional Wordpress admin js/css files are situated in /wordpress-admin/*. I'd make certain your files are put in accordance with that path.