I don't find a J.E.Sanford with the 34th OVI but NPS CWS&SS does show:

Jared E. Sanford
Regiment Name 38th Ohio Infantry
Side Union
Company C
Soldier's Rank_In Pvt.
Soldier's Rank_Out Pvt.
Film Number M552 roll 94

38th Regiment, Ohio Infantry
Organized at Defiance, Ohio, September 1, 1861. Ordered to Nicholasville, Ky., September 1. At Camp Dick Robinson, Ky., till October 19. March to relief of Wild Cat October 19-21. March to Somerset, Ky., and duty there till January, 1862. Attached to 1st Brigade, Army of the Ohio, October-November, 1861. 1st Brigade, 1st Division, Army of the Ohio, to September, 1862. 1st Brigade, 1st Division, 3rd Army Corps, Army of the Ohio, to November, 1862. 1st Brigade, 3rd Division (Centre), 14th Army Corps, Army of the Cumberland, to January, 1863. 1st Brigade, 3rd Division, 14th Army Corps, to October, 1863. 3rd Brigade, 3rd Division, 14th Army Corps, to July, 1865.

SERVICE.-Advance on Camp Hamilton, Ky., January 1-17, 1862. Battle of Mill Springs, Ky., January 19-20. Moved to Louisville, Ky., February 10-16; thence to Nashville, Tenn., via Ohio and Cumberland Rivers February 18-March 2. March to Savannah, Tenn., March 20-April 8. Advance on and siege of Corinth, Miss., April 29-May 30. Pursuit to Booneville June 1-6. March to Iuka, Miss., June 22; thence to Tuscumbia, Ala., June 26. Moved to Huntsville, Ala., July 19-22; thence to Deckard, Tenn., July 27. Decatur, Ala., August 7 (Detachment). March to Louisville, Ky., in pursuit of Bragg August 21-September 26. Pursuit of Bragg into Kentucky October 1-15. Battle of Perryville, Ky., October 8. March to Nashville, Tenn., October 16-November 7, and duty there till December 26. Advance on Murfreesboro December 26-30. Battle of Stone's River December 30-31, 1862, and January 1-3, 1863. Duty at Murfreesboro till March, and at Triune till June. Expedition toward Columbia March 4-14. Middle Tennessee (or Tullahoma) Campaign June 23-July 7. Hoover's Gap June 24-26. Occupation of Middle Tennessee till August 16. Passage of the Cumberland Mountains and Tennessee River and Chickamauga (Ga.) Campaign August 16-September 22. Conducting trains of the army from the Cumberland to Chattanooga during battle of Chickamauga, Ga., Chattanooga, Tenn., September 25-26. Siege of Chattanooga September 26-November 23. Chattanooga-Ringgold Campaign November 23-27. Orchard Knob November 23-24. Mission Ridge November 25. Regiment re-enlisted December, 1863. Atlanta (Ga.) Campaign May 1 to September 8, 1864. Demonstrations on Rocky Faced Ridge May 8-11. Buzzard's Roost Gap May 8-9. Battle of Resaca May 14-15. Advance on Dallas May 18-25. Operations on line of Pumpkin Vine Creek and battles about Dallas, New Hope Church and Allatoona Hills May 25-June 5. Ackworth June 4. Operations about Marietta and against Kenesaw Mountain June 10-July 2. Pine Hill June 11-14. Lost Mountain June 15-17. Assault on Kenesaw June 27. Ruff's Station July 4. Chattahoochie River July 5-17. Peach Tree Creek July 19-20. Siege of Atlanta July 22-August 25. Utoy Creek August 5-7. Flank movement on Jonesboro August 25-30. Battle of Jonesboro August 31-September 1. Operations against Hood in North Georgia and North Alabama September 29-November 3. March to the sea November 15-December 10. Siege of Savannah December 10-21. Campaign of the Carolinas January to April, 1865. Fayetteville, N. C. Battle of Bentonville March 19-21. Occupation of Goldsboro March 24. Advance on Raleigh April 10-14. Occupation of Raleigh April 14. Bennett's House April 26. Surrender of Johnston and his army. March to Washington, D. C., via Richmond, Va., April 29-May 19. Grand Review May 24. Moved to Louisville, Ky., June 12. Mustered out July 12, 1865.

Regiment lost during service 8 Officers and 132 Enlisted men killed and mortally wounded and 2 Officers and 227 Enlisted men by disease. Total 369.

U.S. Civil War Soldiers, 1861-1865
about Jared E. Sanford
Name: Jared E. Sanford
Side: Union
Regiment State/Origin: Ohio
Regiment Name: 38 Ohio Infantry
Regiment Name Expanded: 38th Regiment, Ohio Infantry
Company: C
Rank In: Private
Rank In Expanded: Private
Rank Out: Private
Rank Out Expanded: Private
Film Number: M552 roll 94

1850 United States Federal Census
about J E Sanford
Name: J E Sanford
Age: 7
Estimated birth year: abt 1843
Birth Place: Ohio
Gender: Male
Home in 1850(City,County,State): Defiance, Defiance, Ohio
Looks like he was the son of Seneca Sanford, age 34,a Clerk,born in Vermont, and his wife Harriet C. Sanford, age 32, born in New York; a sister, C.L., age 5, and a brother, R.A., age 4. All the children were born in Ohio.

Seneca Alonzo Sanford
Birth: 9 JUN 1816 in Shoreham, VT
Death: 21 OCT 1893 in Chicago, IL
Note: Resided in Stryker, Ohio.
Father: Linus SANFORD b: 14 JAN 1786
Mother: Sally PERKINS b: 22 NOV 1790

Spouse: Harriet Cecelia BOYDEN
Birth: 25 JUL 1818 in Canton, St. Lawrence County, NY Death: 17 MAR 1861 in Stryker, OH
Father: William BOYDEN

Children
Jared Eugene SANFORD b: 10 NOV 1842 in Farmer, OH
Calista Leonora SANFORD b: 14 JUL 1844 in Farmer, OH
Roswell Alonzo SANFORD b: 19 DEC 1845 in Farmer, OH
Florence Maria SANFORD b: 17 JAN 1851 in Defiance, OH
Clara Augusta SANFORD b: 13 DEC 1853 in Fort Wayne, IN
Augustus Boyden SANFORD b: 21 NOV 1859

Name: Jared Eugene SANFORD
Birth: 10 NOV 1842 in Farmer, OH
Death: 13 MAR 1900 in Chicago, IL
Note: Jared enlisted in the 38th Regiment Ohio Volunteers and served until the close of the war. In 1866 he removed to Chicago, Illinois and engaged in the mercantile business. Later he took a position with J. V. Farwell Company, and held that position until his death.

Marriage 1 Laura E. FURLONG b: 28 JUN 1848 in Portland, ME
Married: 2 FEB 1869 2
Children
Lulu May SANFORD b: 27 MAR 1872 in Chicago, IL
Roswell E. SANFORD b: 23 MAR 1875 in Chicago, IL
Alfred Peck SANFORD b: 28 SEP 1879 in Chicago, IL
[Note: Proprietor of the Commercial Hotel at Texhoma, Oklahoma.]

Marriage 2 Emma C. MORSE b: 3 APR 1856 in Aztalan, Jefferson County, WI
Married: 19 OCT 1887
Children
Allene M. SANFORD b: 13 AUG 1888 in Chicago, IL
Hennem M. SANFORD b: 7 FEB 1892 in Chicago, IL

Marriage 3 Edith PERSHING b: 5 SEP 1865 in West Salem, OH
Married: 10 OCT 1894 2
Children
George D. SANFORD b: 24 NOV 1898 in Chicago, IL
Frank A. SANFORD b: 24 NOV 1898 in Chicago, IL

Sources:
Title: Thomas Sanford, the Emigrant to New England. Ancestry, Life and Descendants. 1632-4
Author: Carlton E. Sanford
Publication: Rutland VT: The Tuttle Company, 1911
Abbrev: Thomas Sanford Genealogy