"I am a Turk: refers more to ethnicity than nationality, when expressing yourself this way the indefinite article is always used.
I am Turkish: refers more to nationality."
benim bildiğim bu.
bir de şöyle bir şey varmış.
"When we refer to a nation or region, we can use:
– the name of the country or region: Turkey, Japan, Germany, Brazil, Asia
– a singular noun that we use for a person from the country or region: a Turk, a Japanese, a German, a Brazilian, an Asian"
dictionary.cambridge.org