Ajax WordPress Login needs to be stayed in current page Url without redirecting

Please try following code it will works for you. Please add this in your functions.php for getting current page URL

    /*Get Current Url */
 function currentUrl( $trim_query_string = false ) {
    $pageURL = (isset( $_SERVER['HTTPS'] ) && $_SERVER['HTTPS'] == 'on') ? "https://" : "http://";
    $pageURL .= $_SERVER["SERVER_NAME"] . $_SERVER["REQUEST_URI"];
    if( ! $trim_query_string ) {
        return $pageURL;
    } else {
        $url = explode( '?', $pageURL );
        return $url[0];
    }
}

Please replace home(); with currentUrl(); It will surely works.