Apple Turkey does not provide service to global warranty iPhones purchased abroad (USA and or EU) even though they are under warranty in Turkey!!!

There is no “global warranty” on any iphone.

The warranty is valid in the country where it was originally sold.

Whoever told you otherwise was misinformed.

it may be possible to have some service done outside the country of original sale. Screen or battery replacements for example, but iphones are region specific.

That's because there is no such thing as a Global Warranty. Apple iPhone Warranty specifically says warranty service may be limited to the country of purchase. You should have purchased your phone in the country you live and use it. If you need warranty service, you'll need to physically bring the phone back the US, where you bought it.