get_post_count_in_taxonomy.php

/**
 * Get Post/Post Type Count in the given Taxonomy
 *
 * @param  $post_type string any post type
 * @param  $taxonomy string any taxonomy
 * @param  $is_exists string NOT EXISTS or EXISTS
 *
 * @return String Number of Post count
 */

function prefix_get_post_count_in_taxonomy($post_type, $taxonomy, $is_exists = 'NOT EXISTS')
{
    global $wpdb;

    $count = $wpdb->get_var(
        "
select COUNT(*) as post_count  
    FROM $wpdb->posts as A 
WHERE $is_exists (
    SELECT 1
    FROM 
         $wpdb->term_relationships as B
             INNER JOIN $wpdb->term_taxonomy as C
                 ON C.term_taxonomy_id = B.term_taxonomy_id
    WHERE C.taxonomy = '$taxonomy'
      AND B.object_id = A.ID
    )                                                    
  AND A.post_type = '$post_type'
  "
    );

    return $count;
}


/**
 * Example
 *
 * Post type: download
 * Taxonomy: download_category
 * Is Exist: EXISTS
 */
echo prefix_get_post_count_in_taxonomy('download', 'download_category', 'EXISTS');