Для агрегированных столбцов вы используете HAVING
, например:
SELECT item.*, count(articles.authorid) AS articlecount
FROM #_authors AS item
LEFT JOIN #_articles AS articles ON (articles.authorid = item.id)
WHERE item.published=1
GROUP BY 1,2,3,4,5,6,7,8 -- assuming there are 8 columns in item
HAVING count(articles.authorid) > 3
ORDER BY 9 DESC -- assuming there are 8 columns in item