Different spelling, but the Roster of Union Soldiers, 1861-1865, shows him as:

Schetler, Barnett KS 13th Inf. Co.D

The Union Army, Vol IV, p.215-216

13th KS Inf Reg raised under President's call of 07/02/1862 for 300,000 volunteers to serve 3 years or the war - recruited during Aug & Sept 1862 from Atchison, Brown, Doniphan, Marshall & Nemaha; organized at Camp Stanton, Atchison & mustered in there 09/20/1862. The men were substantial citizens, mostly farmers. Oct 1862, marched to Leavensworth & Fort Scott & joined Gen Blunt at Old Fort Wayne, Indian Territory & was part of the Army of the Frontier. Moved to Camp Ewing, to Camp Bowen, AR & later to Camp Babcock on Lindsay's Prairie, AR. Weer's [2nd] Brigade, Blunt's [1st] Divison. Engaged at Cane Hill with no loss. Pursued Marmaduke; returned to Cane Hill & encamped there until battle of Prairie Grove, with losses of 8 men killed, 3 officers & 40 men wounded & 5 MIA. Returned to Cane Hill & encamped there to 12/27/1862; moved to Van Buren in extremely cold weather. Moved to Elm Springs & encamped there to 01/07/1863; forced march to Springfield, MO. Remained here to Spring, pulling garrison & escort duty. 05/19/1863 moved to Fort Scott; Dry Wood & encamped pulling outpost duty duty for 2 months, while men went home on 20 days furlough. Took the field again 08/03/1863 in Gen Blunt's campaign against irregulars of Cooper, Cabell, Steele & Stand Watie, driving them to the Red River & capturing Fort Smith. Marched over 400 miles in August, 200 during last 10 days of the month. Ordered to Webber's Falls, Indian Territory for 2 weeks; moved to Scullyville, Indian Territory for outpost & scout duty to 10/06/1863. Moved to Van Buren, AR for winter quarters. March 1864 to Fort Smith, AR for garrison duty. The year 1864 spent in garrison and scout duty. March 1865 moved to Little Rock, AR for guard & provost duty to 06/26/1865 when it mustered out. Discharged at Fort Leavenworth 07/13/1865.
Lost during service, 3 officers & 20 men killed or died of wounds; 1 officer & 104 men died of disease, accident or other causes.