Hi I'm a white mum to a dual heritage (white British/Black African) young man.
To be blunt what your son looks like is going to have a huge impact on how he experiences life.
We have had some interesting conversations in the last few days, my son is beginning to realise that he is neither white nor black but occupies a space in between. Although he is not very dark skinned, he does have Afro hair so what you see is a young black man ( he is 16) so this is how he is labelled. He thinks this is very unfair as it doesnt acknowledge his white half.
My own view, as a white person, is also that both parts matter, but I can't ignore the wider societal pressures.
I also take a pragmatic approach in that we live in England, not Africa, in a majority white culture. But I also recognise that culture, particularly youth culture is very fluid and a lot is shared across cultures - thinking about music, fashion, sport, popular TV etc. There is no point trying to get him to eat African food when want he wants is pizza, or listen to certain music when he listens to rap.
There is a lot you can do to acknowledge his heritage without going down the lets have a full blown Turkish night every month route.
If you talk to him about being adopted, then his Turkish heritage should be a natural part of those talks. If he reads look for Turkish folk tales, there is a lot of Middle Eastern/Turkish food that you could introduce that is fairly mainstream these days - kebabs, humous, tabbouleh, baklava. Maybe look for some textiles that you could use around the house such as hamman towels.
It doesnt have to be a big deal if you just make it part of life.
In our home, because I travelled a lot in various parts of Africa before I adopted my son I have a lot of stuff around, its just there, we don't necessarily talk about it, but it acknowledges other cultures. This includes textiles used as tablecloths and bed throws, cushion covers framed photos from my trips, my handbags(!), fruit bowls, books, original artwork. Sometimes he will ask where I got something so that promps a discussion, particularly if its something from the country his dad comes from.
Its not possible now of course, but in future think about a family holiday to Turkey. I havent been able to take my son to the relevant country but we have been to Gambia, this was really helpful as although its a different culture, there are some common things such as drumming which he was able to participate in. I think it gave him a real sense of his Africaness for want of a better word.
Whether we like it or not, our adopted children are different, but different is not bad or negative. Its just different and can be celebrated.