// prepare our arguments for the query
$args = json_decode( stripslashes( $_POST['query'] ), true );
$args['paged'] = $_POST['page'] + 1; // we need next page to be loaded
$args['post_status'] = 'publish';

// it is always better to use WP_Query but not here
query_posts( $args );

if( have_posts() ) :

    // run the loop
    while( have_posts() ): the_post();

        // look into your theme code how the posts are inserted, but you can use your own HTML of course
        // do you remember? - my example is adapted for Twenty Seventeen theme
        get_template_part( 'template-parts/post/content', get_post_format() );
        // for the test purposes comment the line above and uncomment the below one
        // the_title();


    endwhile;

endif;
die; // here we exit the script and even no wp_reset_query() required!