function common_cats($att){
$args = array(
'category__and' => $att['category'], //must use category id
'tag__in' => $att['tag'], //must use tag id for this field
'posts_per_page' => $att['posts_per_page']); //get all posts
$posts = get_posts($args);
$output = "<ul>";
foreach ($posts as $post) :
$output .= "<li>".get_the_title(). "</li>";
endforeach;
$output .= "</ul>";
return $output;
}
add_shortcode('commoncats', 'common_cats');
use [commoncats] where you like to show the output of the above code.
above code will return a list of titles.