"My brother is a Turk, but not me."
Translation:Mein Bruder ist Türke, aber ich nicht.
It would be "ein Türke" because "der Türke" (and the brother) is masculine (and male). A female Turk would be "die / eine Türkin". But you don't need an article to describe someone's nationality (or profession), so it's just "Mein Bruder ist Türke" - it's actually equivalent to "My brother is Turkish" in English, only we don't use the adjective ("türkisch") in German, but the noun ("Türke").
"...aber nicht ich" is a more unusual word order, but it works. It changes the connotation/emphasis a bit, cf.:
You could say "Mein Bruder ist Türke, nicht ich" to correct someone: "It's my brother who's Turkish, not me." With "Mein Bruder ist Türke, ich nicht", you just neutrally state that "my brother is Turkish and I'm not".
The more usual word order that you can use in all situations, though, is "...aber ich nicht", so I think this is what Duolingo should teach here.
Why so often Turkish? Surely there other ethnicities in Germany? Or is it used often in all duo languages?
Or, in this case, "...aber ich bin keiner." (short for "ich bin kein Türke")
But for adjectives you need to use quis_lib_duo's way: "Mein Bruder ist klug, aber ich (bin es) nicht." (short for "ich bin nicht klug")
No, "sondern" is only used when the negation is in the other part of the sentence/statement: "nicht mein Bruder, sondern ich"; "Wir fahren nicht mit dem Zug, sondern wir laufen" ("We're not going by train, but we are walking [instead]")
Note that "sondern" implies "one thing instead of another". Cf. this recent discussion; to reuse MaxEm's example:
"Ich habe kein Bier, aber [ich habe] Wein" = I don't have beer, but I do have wine (e.g.: I'm a pub owner and you asked me for beer, which I don't have; I'm assuming that the next best thing I can offer you is wine. I (probably) have a range of other drinks as well.)
"Ich habe kein Bier, sondern Wein" = It's not beer I have, but wine (e.g.: I promised to bring drinks to the party. You thought I would bring beer, but I've got to correct your assumption: I've actually brought wine, not beer.)
So there's a small difference between "Mein Bruder ist kein Türke, aber ich" and "Nicht mein Bruder ist Türke, sondern ich": "...sondern ich" implies that you knew that one of us is a Turk, but you thought it was my brother, when actually it's me. "...aber ich" implies that you were speculating about my brother being a Turk; I tell you that he isn't and add that I, however, happen to be a Turk.
Because it's in the nominative case; some say that "...but not me" is actually incorrect here and it should be "...but not I". You could say "...but I am not" instead. (I'm leaving that for native speakers to discuss...)
Although "me" is used in the English sentence, there's no reason for an accusative anywhere: "My brother is a Turk" - "my brother" is the subject, thus nominative case; "a Turk" is what my brother is, the Turk and the brother are identical, the Turk is not an object, so: nominative case as well; and "I" is basically an alternative subject, or the subject of a second sentence: "...but I am not a Turk", thus nominative case.
Riight, i think i get it. So it would be better to translate it to 'but I am not'?
Well, not really, I just used it to explain why "...but not I" / "...aber ich nicht" is nominative case (as opposed to what "...but not me" might suggest).
I'd just do the simple thing and translate "aber ich nicht" with "but not me/I", and vice versa.
In addition to that:
"...but I am not" doesn't have an exact literal equivalent in German ("...aber ich bin es nicht" doesn't work).
"...aber ich bin keiner" doesn't have an exact literal equivalent in English ("...but I am not one" doesn't work).
However, I think "...but I am not" and "...aber ich bin keiner" share the same tone/emphasis, so I'd use those two phrases as translations of each other.