Can you fly through Northern Cyprus airport with a visa from the Republic of Cyprus, any EU country, or Schengen?

Under the Republic of Cyprus law, if you have a passport from one of the EU countries, you can fly in and out of any airport on the island, including Northern Cyprus Airport. If you arrived in the Republic of Cyprus at the airport of Larnaca or Paphos with a Schengen, the Republic of Cyprus, or one of the EU countries visa, then by law, you need to leave the country through one of the southern airports. If you fly out through the northern Ercan airport, you will violate the law - it means for the Republic of Cyprus that you have not left the country. Therefore, this option is not desirable though no one will prevent your departure.

If you arrive in Northern Cyprus at Ercan Airport, you can freely cross the border between the southern and northern parts of Cyprus. But again, you need a Cypriot visa, a visa from one of the EU countries (Bulgaria, Romania, Croatia), or a Schengen visa. The only thing is you have to fly out from the airport where you arrived.