I'm not aware of any uniquely Cherokee DNA though DNA could identify genes that are common to Native Americans. Cherokee is a nationality, a culture, and a language and like most all nations, includes "naturalized citizens" of different heritage. There are of course many of Cherokee heritage who are no longer citizens of the Cherokee Nation, much like Americans of Italian heritage are no long citizens of Italy.

During the American Civil War, the Confederate Cherokee regiments included many non-Indians from Arkansas and Missouri. They were not exclusively made up of Cherokee citizens.

Ken