half-foreign, fourth-foreign...

Yes. You could also use quarter instead of fourth.

It seems to me that "foreign" is different in this respect than a specific foreign identity. To me, "foreign" means "from another country." I might call a child with one parent from China and one American parent "half-Chinese," but if the child was born and raised in the U.S. I would not consider that child "foreign" at all. I find the idea of "half foreign" or "one-quarter foreign" odd.

khoffI find the idea of "half foreign" or "one-quarter foreign" odd.

I agree, I have never come across these expressions. If I were to come across them, I would assume they were uttered by a non-native speaker.

I have seen "eighth-foreign" in Edna O'Brien's short story. She is quite old, as you might know, so maybe it was common in the past. Her language is full of old words and expressions.

marquezI have seen "eighth-foreign" in Edna O'Brien's short story.

There is often a world of difference between the language used by gifted novelists and the language used by us lesser mortals. Granted that, I (a lesser mortal) might use 'eighth-foreign' in certain situations. Such situations would be rare, and would eflect little credit on me.

I've identified another reason I don't like it. If I heard someone refer to people as as "half-foreign" or "one-quarter foreign," I would assume that the speaker probably doesn't like foreign people.