If the 1860 Federal Census is your Jasper Dennard, its unlikely the CSA record for J. H. Dennard was the man you seek.
1860 Federal Census
Jasper Denard [Jasper Dennard]
Birth Year: abt 1824
Birth Place: Fla
Home in 1860: Western District, Milam, Texas
FOLD3 only has one "J" Dennard from Texas who enlisted in the Confederate army at Tarrant County in December 1861. J. H. Dennard was a 26 years old merchant born in Georgia when he enlisted in Company E of Young's 12th Tx Infantry. In November 1862 he transferred to Company G of Parson's 12th Texas Cavalry. On February 24, 1863 he was given a medical discharge due to pulmonary problems. No further records.
There was a D. J. Denard in Company F of Young's Rgt, but he Died May 9, 1862.
No other names with similar spellings of Dennard, Denard, Dennar, etc found.
I also checked in FOLD3 the three Texas Regiments at the Battle of Gettysburg (1st, 4th, and 5th Tx Infantry). None of them list anyone with a name spelled even close to "Dennard."