From the CWS&S website:

Albert Beale (First_Last)
Regiment Name 2 Cherokee Mounted Volunteers.
Side Confederate
Company E
Soldier's Rank_In Private
Soldier's Rank_Out Private
Alternate Name
Notes
Film Number M818 roll 2

You should post on the Indian Territory Message Board. There are participants on that board that have researched Bryan's Battalion. However, like all Indian Territory units, records are scant, especially after 1863.

Bryan's Battalion is a Cherokee Cavalry Battalion that became part of the 2nd Cherokee Mounted Volunteers (Adair's Regiment) in 1863.

There were a number of Arkansas men in the Cherokee Units. Some were Cherokee who had been living in Arkansas but many of these were white men who didn't want to be sent east of the Mississippi -- the Indian Troops by treaty could not be sent out of their Nations without their approval so the whites in these units knew they could stay closer to home.

ORGANIZATION. Joel M. Bryan was authorized by Brig.
General Albert Pike to raise 100 men or more as partisan rangers
during the summer of 1862. The company (A) was mustered in
Fort Davis, Canadian District, Cherokee Nation, July 20, 1862. [Fort Davis was in the Creek Nation just west of the Cherokee Boundary. KM]
Bryan proceeded to recruit another four companies, and was ordered
by Maj. General Thomas C. Hindman to organize the force
into a battalion, which was done September 13, 1862. Records indicate
that the enlistment term was three years.
By order of Brig. General Douglas H. Cooper, the battalion
was on February 3, 1863, consolidated with 5 companies attached
to Watie's 1st Cherokee Mounted Volunteers to form the 2nd
(Adair's) Cherokee Mounted Volunteers

By Lars Gjertveit and on the internet at
from http://www.thepeoplespaths.net/history/CherConfed.htm

As a side note, the eastern half of Oklahoma was always Indian Territory until Oklahoma Statehood in 1907. Oklahoma Territory was not created until well after the war and was only the western half of present Oklahoma.