Replace or reduce sugar in milk?
So, there's no method to get sugar out of milk, as far as I know.  You can look for milk products where some of the sugar is used up (fermented, like Chris H mentioned), but this will significantly change taste and texture - sugar is a major part of what milk is, fats and sugars and proteins, and you're removing most of the actual substance.

You're likely to do better with an unsweetened nut milk or rice milk, especially if you make your own so you can tweak to taste.  These may have more fats, depending on your choice of recipe, but will likely have sugar closer to your desired range

One thing you might try, if you're really determined, is to dilute your milk (maybe up to half) and add artificial sweeteners.  You'll still get some of the flavor components from the added milk, and some sweetening to make up the difference in taste, but there will be less sugar because the actual amount of milk is less. Hopefully the added artificial sweetener might make it taste less watery, but maybe add just a half a pinch of salt if it still tastes too thin.  in the end, ~6g sugar per cup, I guess?

Another possibility is to use unflavored whey powder to flavor the diluting water (again, probably no more than half of your "milk"), then adding artificial sweetener to taste.  The whey should have some of the flavors from the proteins in milk, and at least from the powder I checked it doesn't have much of the sugar or fat you're objecting to.  It might help the diluted milk taste less watery. ~7g sugar, because I think the whey powder has a gram and a half per serving.

Final possibility I thought of - you can maybe grab some creamer powder and use that to flavor your diluted milk (again, not more than half and sweeten to taste).  Or even use it on its own, if the flavor works for you.  The amount of sugar isn't stated, but it has to be under 1g because that's all the carbs there are per serving - though it does add a half gram of fat back in.