How old is he again? It's good in a way, if the vet says there is nothing wrong with him. Can I ask what the weather is like? (I can't remember which country you're in
). In hot weather, hamsters can sometimes have a bit of a moult.
I wouldn't give vitamin drops personally - not in their water anyway. But if there are skin and fur issues, I usually give a pinch of linseeds every day. After 6 weeks to two months, you should notice their fur improving or even regrowing in places. I assume it's partly the vitamin e in the linseeds but it's more than that, as they are a whole food with various oils etc that affect the whole body positively.
Additionally, if vitamins are needed, I give a pinch of hemp seeds daily - these are supposed to contain all vitamins and minerals needed, in a more natural way - and hamsters seem to like them - they are sort of nutty. They lick up both seeds. I usually put out a separate little dish just for the hemp seeds and linseeds (eg a jar lid) - and put a pinch of one at one side and a pinch of the other at the other side. But I would start with just linseeds for now, every day. Otherwise sometimes they only eat one and not the other. If the vitamin drops can go in food you could give those as well for a while, plus the linseeds. Although personally I would just give the linseeds, then after 6 weeks or so introduce the hemp seeds as well.
The itching - it is normal for hamsters to scratch a lot - it's part of grooming and normal. If he is scratching so much it is causing raw and open areas then that is not normal. But if it isn't then it could just be him grooming a lot. They sometimes groom more at some times than others.
I can't remember what bedding you use as the other possibility is an allergy. I'm sorry I haven't read back! So can't remember if this has been mentioned before. Hamsters can be allergic to any type of wood - whether it's hardwood or softwood. It's a possibility if he has anything other than paper bedding (which is hypoallergenic).
Did the vet do a skin scraping for mites at all? I assume if he thought it was mites he would have prescribed something for them though.