$("#userLogin").click(function(){
    var usrEmail = $("#usr_email").val();
    var usrPassword = $("#usr_password").val();
    $.ajax({
        xhrFields: {
            withCredentials: true
        },
        url: 'http://username:password@website.com/APIs/public/login',
        data: {email: usrEmail, password:usrPassword},
        type: 'GET',
        error: function (request, error) {
            console.log(arguments);
        },
        success: function(data) {
            alert(data);
        }
    });
    event.preventDefault();
});

<IfModule mod_headers.c>
    Header set Access-Control-Allow-Origin "*"
    Header set Access-Control-Allow-Credentials true
</IfModule>

"NS_ERROR_DOM_BAD_URI: Access to restricted URI denied"