I've found more genealogical information that makes it clear that #3 and #9 in my previous post are the same Uriah Wise. This information allows me to eliminate him as a possible Civil War soldier, because it's known that he did not serve in the military. Source: Kensall D. Wise, Millers and Wheelwrights: the Penn's Creek Wises of Pennsylvania, Ohio, and Michigan.

I think that #4 Uriah Shepherd Wise (son of Hamilton Jefferson Wise & Catherine Shepherd) could have served in the Pioneer Brigades as well as the 64th OH Infantry since the Pioneers were recruited from existing regiments and both units were present at Stones River. This Uriah S. Wise married Mary J. "Jennie" Clendenning.

I've tried to determine the identity of each soldier & veteran; but I haven't yet identified the family of the soldier from the 6th KS Cavalry. As far as I can tell, Uriah #10 served with 210 PA Infantry, lived in KS in 1880, then moved to OH where he died in 1923. Uriah #8 was born in AR or MO, but served with 6th OH Cavalry & was buried at Marshall Co., IN. Uriah #2 had a son, John Alexander Wise, who moved from Port Royal, PA to Baldwin, KS about 1873. It's all very confusing, especially since several of these men appear to share common ancestors.

Civil War Soldiers (All fought with the Union)
2) Private Uriah Wise, Co. F, 171 PA Infantry (Drafted Militia) (b. PA, lived in PA, parents b. PA)
Regiment also included Musician Absalom Wise & Private Emanuel Wise in Co. F

10) Private Uriah A. Wise, 210 PA Infantry (b. PA, lived in KS & OH, parents b. PA)

Regiment also included Pvt./Cpl. John A. Wise in Co. G

4) Sgt/Private Uriah S. Wise, Co. F, 64th OH Infantry (b. IN, lived in OH, parents b. PA)

Participated in Battle of Stones River

Regiment also included Pvt. Napoleon Wise in Co. A

#8 Private Urias J. Wise, Co. B, 6th OH Cavalry
(b. MO, lived in AR & MO, buried in IN)

Fought in northern Virginia, including Upperville, VA, 21 June 1862;
Manassas Junction, 14 Oct 1862

Regiment also included Privates John & Joseph Wise in Co. L
?) Private Uriah/Uria Wise, Co. H & G, 6th KS Cavalry

Regiment also included Privates Edward & Samuel Wise
& Corpl. Joseph Wise/Weise in Co A, M, F

4?) Private Uriah S. Wise, Co. B, 3rd Battalion, Pioneer Brigade

Organized by Rosecrans from various regiments, 21st corps, Army of the Cumberland
(aka Army of the Ohio); participated in Battle of Stones River

No other soldiers with Wise surname in this unit

#3 & #9 are the same man; not a Civil War soldier & possibly a conscientious objector

1890 Veterans
1) Uriah Wise, Chambersburg, Franklin, PA // US Soldier (He & wife Hannah lived near Upperville, VA in 1870)

2) Uriah Wise (Sarah J.), Turbett, Juniata, PA // Private F 171 PA Infantry

4) Uriah H. Wise/Uriah Shepherd Wise (widow Mary J.), Van Wert, Van Wert, OH // Sgt/Private F 64 OH Inf (son of H.J. & Catherine)

10) Urias Wise, Montgomery, Wood, OH // Private K 210 PA Infantry

(son or grandson of Uriah W. Wise of Washington Co., PA?)

1891 Civil War pension file
4) Uriah S. Wise, F 64 OH Infantry, Sgt/Private (George W. Wise, minor child)

1892 Civil War pension file
2) Sarah J. Wise, widow of Uriah Wise, F 171 PA Infantry (Sarah J. Noss?)