$(document).ready(function(){
$('#form').submit(function(e){
 e.preventDefault()

$.ajax({
    type: 'POST',
    url: 'ajax/login',
    dataType: 'text',
    data: { username: $('#username').val(),
    password: $('#password').val() },
    error: function(req, text, error) {
        alert('Ошибка AJAX: ' + text + ' | ' + error);
    },
    success: function(response) {
if (response == "1") { alert('1') }
if (response == "2") { alert('2') }
if (response == "3") { alert('3') }
else { alert(' неправильный логин или пароль') }
},
error: function(response) {

}
});
return false;
})

});



<?php
require "../config.php";

$login = $_POST["username"];
$pass = $_POST["password"];
$auth = "1";
if (isset($_POST["signin"])) {

$username = mysqli_real_escape_string($connect, $login);
$password = hash('sha256', $pass);
$check    = mysqli_query($connect, "SELECT username, password FROM `players`
WHERE `username`='$username' AND password='$password'");
if (mysqli_num_rows($check) > 0) {
    session_start();
    $_SESSION['username'] = $username;
    $auth = "2";
} else {
    $auth = "3";
}

}
echo $auth;
?>