Genom att ställa in radnumret med variabler och sedan filtrera resultatet så att det bara visar rad 1-3 borde fungera
SET @last_objectId = 0;
SET @count_objectId = 0;
SELECT id, name, image FROM (
SELECT
user.id,
user.name,
user.image,
@count_objectId := IF(@last_objectId = rating.objectId, @count_objectId, 0) + 1 AS rating_row_number,
@last_objectId := rating.objectId
FROM users
LEFT JOIN ratings ON (ratings.userid = user.id)
WHERE
rating.rating > 0 AND
rating.objectId IN (1,2,3,4)
ORDER BY rating.objectId
) AS subquery WHERE rating_row_number <= 3;