function login(){
var username = document.getElementById("username").value;
var password = document.getElementById("password").value;
var dataString = 'username1=' + username + '&password1=' + password;
if (username == '' || login == ''){
    window.alert("Please fill in username or password.");
}
else{
    $.ajax({
        type: "POST",
        url: "login.php",
        data: dataString,
        cache: false,
        crossDomain : true,
        success: function(response) {
            if (response.status == 200) {
                window.location = 'http://localhost/site.html';
            }
            else {
                window.alert("The password or username you have entered is not valid");
            }
        }
    });
}
return false;

<?php
header('Access-Control-Allow-Origin: *');
header('Access-Control-Allow-Methods: GET, POST, PATCH, PUT, DELETE, OPTIONS');
header('Access-Control-Allow-Headers: Origin, Content-Type, X-Auth-Token');
$password2 = $_POST['password1'];
$username2 = $_POST['username1'];
$connection = mysqli_connect("localhost", "root", "password", "database") or die("Unable to connect to MySQL");
$query = mysqli_query($connection, "SELECT * FROM users where username = '$username2' AND password = '$password2'") or die(mysqli_error($connection));
$row = mysqli_fetch_array($query, MYSQLI_BOTH) or die(mysqli_error($connection));
if(!empty($row['username']) AND !empty($row['password'])) {
    session_start();
    $_SESSION['username'] = $username2;
    http_response_code(200);
    echo "Successful Login";
    exit;
}
else{
    http_response_code(403);
    echo "The password or username you have entered is not valid";
}
mysqli_close($connection);
?>