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The best source for authorized Apple retailers will be Apple itself. Apple's Turkish website links you to sales information in Turkish or English. A search for turns up listings and a map for dozens of authorized retailers within Ankara, and dozens more in nearby cities such as Kirikkale and Γankiri. Additionally, Apple's Online Store has been operating in Turkey since autumn 2013.
There is at this writing only one official Apple Store in Turkey, in the Zorlu Center in Istanbul. According to the ElmaDergisi blog, a second Istanbul store is under construction in the Akasya Shopping Center, to open autumn 2014. An earlier post in that blog stated that stores were planned for Ankara and Δ°zmir in 2015, a rumor endlessly repeated elsewhere, but one still lacking an authoritative confirmation.
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Note that list on Apple's page seems outdated. f.i. ElectroWorld closed all their stores in Turkey but they are still listed on Apple's website.
In Ankara, you can pretty much find one of the authorized retailers in any shopping center/mall. Either MediaMarkt, D&R, TeknoSA, Gold Computer or Bimeks. At least one of these operate on any mall you pick. Though if you do not speak Turkish, i recommend D&R or MediaMarkt, you have higher chances of finding someone who speaks English.
If you can comment below about where you are staying or where you visit/go to during the day, i can direct you to nearest place you can find an iPod.