Ordinarily when soldiers of the Federal government held a battlefield after the fighting ending, Federal dead could be identified and buried. After the war these and any other Federal dead found nearby were collected and reinterred in National cemeteries.
Of course the reverse is not true.
In any case, look for Federal soldiers in National cemeteries. For anyone else, that's the wrong place to look -- except in rare and unusual circumstances, Confederates will not be found there.