How to use wp query in my custom page without including header and footer in wordpress

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You have an option to use require() method in PHP. It doesn’t require to load header/footer in renderdata.php in order to use WP_Query() query class.

add_action( 'wp_ajax_nopriv_aj_page', 'my_aj_page' );
add_action( 'wp_ajax_aj_page', 'my_aj_page' );

function my_aj_page() {
    require('ajaxpage/renderdata.php');
    die();
}