Company K was part of the infantry regiment from which the Legion was formed. A legion like Thomas' Legion was made up of infantry, cavalry, and artillery. They were split up during much of the war. Some served in east Tennessee, western NC, and southwest Virginia. Some were with Early in the Shenandoah in 1864.
It's probably out of print, but a great resource is "Storm In The Mountains" by Vernon Crow. I was fortunate enough to get one in the early 1980's.