This took a certain amount of digging, and I'm not completely certain that it qualifies on my geographical criteria - several reviewers think it is set in Bosnia, though the author seems clear that it is in Kosovo. It is the first in a series of six thrillers by the son of one of Ronald Reagan's Secretaries of State, himself now a military policy wonk. Published in 2001, it is:
Secret Sanction, by Brian F. Haig
In second place on Goodreads, fourth on LT, is a 2009 book about a girl whose family are expelled from Kosovo during the 1998-99 conflict and her difficulties in adapting to American society, by a very well-known author. I suspect it fails my geographical criterion, but for the record it is:
The Day of the Pelican, by Katherine Paterson
In third place on both systems is a 2006 book with almost exactly the same theme but for much younger readers. Again, I suspect it fails my geographical criterion, but it is:
Drita, My Homegirl, by Jenny Lombard
In second place on LT, but fifth on GR, is the most authoritative non-fiction work on Kosovo that you are likely to find, a 1998 history of the country:
Kosovo: A Short History, by Noel Malcolm
And fourth on GR, fifth on LT, is another non-fiction book, a 2003 memoir about teaching English in Pristina shortly after the end of the conflict:
The Hemingway Book Club of Kosovo, by Paula Huntley
Bubbling under: Tim Judah.