每个用户id限制3行

您可以使用 row_number() 在子查询/派生表内:

select users_id, users_name, messages_id, messages_name
from (
  SELECT users.id as users_id, users.name as users_name, messages.id as messages_id, messages.name as messages_name, messages.sent_at
    , row_number() over (partition by users.id order by messages.sent_at) as rn
  FROM messages
  INNER JOIN users on messages.user_id = users.id
  WHERE users.active = true
) as sub
where rn < 4
ORDER BY users_id, sent_at