Upvote:1
Is there some kind of a rule/minimum days of stay in the Schengen area for an individual before he/she can leave the Schengen, whatsoever?
No, of course not. Plenty of people enter the Schengen area for a few hours, for example during a long layover. However be aware that you will have an exit stamp next to your entry stamp, so it would be easy to infer you immediately left if someone takes a look at your passport.
Will that be somewhat problematic?
Neither the Schengen border guards nor the visa issuing agencies in the respective countries care about your visits, as long as they're within the duration of the visa. However we have no way of knowing if you'll get in trouble with whoever issued you the scholarship.