drinking milk has nothing to do with feeding, it cannot enhance milk production.
The first n foremost thing that matters is how many times u feed, suction is a natural stimulation which causes the milk to flow, the more the baby sucks the more milk is produced, no matter the baby is hungry or not he/she would definately start sucking when brought near the breast n make sure ur in the correct position because at times if the mother's position is not comfortable for the baby he/she would not suck hence milk production would be slower
If u think ur baby is full u can buy a suction pump n use it, u can also store that milk if you want.
keep in mind that some people also restrict the use of milk during nursing, so milk production has nothing to do with drinking milk
just maintain a balanced diet, fresh coco water can also increase milk production, u can use sesame seeds as they are rich in calcium, fish also enhances milk production, but remember all of this would not work if breasts are not stimulated. Remember if a woman does not feed for 2 or 3 days the milk stops coming