I have a Schengen visa for Hungary from 24-28 March, but have air tickets that depart on 29th of March at 6 pm.
Will I be allowed or is there any problem if I overstayed 1 day?
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You will likely be able to board the plane, but unlikely to be allowed back into the Schengen again. If at all possible, change the flight back, or get a new flight, that will allow you to leave on the 28th.