There is a historical example of a genetic trait associated with nobility, although neither so exclusive or desirable as your question suggests - the Hapsburg Lip or Hapsburg Jaw. The Hapsburg family prospered as much by marriage and inheritance as by conquest, so preservation of their lineage was a dynastic priority. Marriages were made within a fairly narrow circle of prestigious families, and when suitable candidates were wanting, incestual matches within the family were not uncommon. The result of these centuries of inbreeding were somewhat predictable. Certain less desirable traits popped up in the bloodline, including a noticeable tendency to a severe under-bite that gave many Hapsburgs a very distinct appearance. The phenomenon found its ultimate expression in the person of Charles II of Spain (the "bewitched"), who in addition to a drastic example of the Hapsburg jaw (seriously, google it), was also a general laundry list of genetic shortcomings - small, weak, lame, epileptic, prematurely bald, allegedly insane, impotent, and generally troll-like. Jaime Lannister is the school-girl dream of noble "breeding"; Charles II was the ugly reality of spending entirely too much time with your cousins.