I think in addition to the other answers it might be beneficial to mention that the way the Schengen area works is there are no borders inside the Schengen area.
Once you’re inside you can go anywhere, it’s like a house where only the entrance door has a lock and the room doors don’t have locks, once you enter through the entrance door you’re in and can go to any room now. But if you want to go to the garden or a neighbour you have now left the house and cannot go to any of the rooms until you re-enter the house again through the main door.
Even though you say that you just wanted to go from Spain to Greece, you didn’t just go from room Spain to room Greece within the house, instead you rather left the house to go to your neighbour (Turkey) on your way there and because of that now to actually get to room Greece you have to re-enter the house (Schengen) and you don’t have permission to enter the house more than one time. But if you wouldn’t have left the house (Schengen) you would have been able to go to as many rooms (Schengen countries) as you liked.
Your thinking seems to be that because you were flying from one country in the Schengen Area to another country in the Schengen area, then you were not really “exiting” Schengen, so should not have been given an exit stamp.
This would be absolutely correct – IF you were catching a flight that went directly from Spain to Greece, or went via another country in the Schengen region (eg, Spain -> Germany -> Greece).
However Turkey is NOT in the Schengen area. Thus your flight actually had you departing the Schengen area as you flew to Turkey, and then re-entering it when you arrived in Greece. This is true even if you were only in transit in Turkey and didn’t actually enter the country – once you walk through immigration in Spain you are deemed to have left the Schengen area.
With only a single entry visa it it not possible to take this flight. Your “single entry” was used when you entered Schengen the first time. Flying to a non-Schengen country (eg, Turkey) and then returning would require a visa, and you didn’t hold one that was still valid so you were correctly denied boarding.
Presuming both of your flights were booked on the same ticket, the airline in Spain should not have actually let you take the flight to Istanbul as you didn’t hold the correct documents for the entire trip – however at the end of the day the responsibility for having the correct documents falls to the traveler.
Turkey is not in the Schengen area, so going from Spain to Turkey is exiting the Schengen area and therefore your passport gets stamped with an exit stamp.
But the exit stamp is actually entirely irrelevant for your problem.
The stamp that’s a problem for you is your entry stamp from when you first entered Spain. This means that your single entry is now spent, and you’re not allowed to enter the Schengen area once more, which you would if you were allowed to fly from Turkey to Greece, as Greece is within the Schengen area.
(If you didn’t have the exit stamp, it would still be obvious that you had in fact left the Schengen area at some time, since you’re currently outside that area rather than still inside).
If you don’t have a visa that’s valid for the itinerary you’re trying to follow, that’s your problem. Not that of the various officials who are correctly administering the rules.
If you entered and left the Schengen Area in Spain to Turkey then your Single entry C-Visa has been used.
A entry stamp for entering the Schengen Area must exist.
Receiving an exit stamp from Spain to Turkey is correct.
An image showing the C-Visa and entry/exit stamps would be helpfull to clarify.
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