Izmir has a higher pop. than Adana and also borders the Mediterranean. Izmir lies on the Aegean, which is a part of the Mediterranean. Whether or not Istanbul counts too is a whole other can of worms. The question should just be replaced with something more clear-cut.
Got everything but sort of cheated on Adana because I looked at a map just to make sure that I had already named every big city on the southern coast (I had, they are Mersin, Antalya, Alanya, Marmaris) and I wanted to see what I was missing. Even though Adana is 50 km away from the coast, I started trying cities that were in the interior of Turkey starting with Gaziantep and then Adana was the 2nd one so I got it. But.... it's not really on the coast, is it? I think the true answer in Antalya or Mersin.