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Hello dear, if he originally drinks milk to put him to sleep at bedtime then he is associating milk with sleep hence when his sleep cycle is in the shallow sleep he wants that association. I would recommend completely cutting milk at bedtime, it needs to before so he doesn't associates. Try to give him incentives like sticker chart and encouragement that he is older wiser etc. Once he wakes up at night keep reminding him of that incentive and try to stay calm but don't give him the milk, if you can do it for three days without succumbing.
Good luck