I dont know exactly if there is direct busses from Adana airport .. But you can be sure that there are many busses from Adana bud terminal to Antakya or Reyhanli...
As traveloturc said, I'm not sure about buses from the airport, but I was in Adana recently, heading to Antakya, and asked around before booking. There are buses going almost every hour with different companies. I used Has Turizm, which has six or seven buses a day, and cost me 23TL booking online at http://eticket.hasturizm.net or you can just turn up at the out of town otogar and pay 25TL. I don't know about Reyhanli, but you can certainly get there from Antakya.
Take a taxi from the airport to the otogar if you are going straight to Antakya. Alternatively, in the centre of Adana on Ziya Pasa Caddesi, all the bus companies have offices where you can buy tickets, and they provide a free minibus service to the otogar in time for your bus.
The best way is take taxi from the Airport to the Otogar (Bus station) fee about 10-15 TL then take bus from Adana to Antakia they called it (Hatay) from there you can take mini bus to Reyhanli .
Hope this help you . Best Wishes
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