Here's an early war image showing cap insignia: small size letters and numerals "93 PV"
This cap insignia was regimental, and not according to any army regulation. Army regulations called only for a company letter on the forage cap, in brass, 1-inch in size. The volunteer units in the Union Army varied their insignias, often including some regimental marking, or none at all. The 93rd example above excludes the company letter. The numbers and letters used appear to be maybe 1/2 inch.
The private here wearing the US Army infantry uniform coat, forage cap, and 1861 pattern sky blue trousers.
George Stevens says that after the Peninsula Campaign, the troops who were assigned to the Sixth Army Corps were rather worse for wear...
Private John Miller of Company F, with corps badge on his forage cap, ca. 1863, of the Sixth Army Corps. The corps badges were mandated at army level after the spring of 1863, made from colored flannel. Miller wearing the flannel fatigue blouse, and forage cap.
The 93rd was with the 3rd Division of the Sixth Army Corps. A blue cross.
Here's a couple more Sixth Corps chaps demonstrating that Miller was wearing his cap badge correctly, the cross, crossways...
The Sixth Corps badges in 1863 were described as "St. Andrews" cross, and worn crossways. In 1864 it was ordered they be a "Greek Cross" and worn straightways, as shown on the monument...
And on some period photographs showing late war corps badges. Charles Marquette (Medal of Honor) of Company F, 93rd PA wears his corps badge on a non-regulation slouch hat in this 1865 photograph:
Marquette wears a jacket, of the type frequently called today a "schuylkill infantry jacket." In fact, just an Army mounted services jacket with the branch trimmings, etc. removed, and the collars, etc. modified for infantrymen to wear when they wanted to.
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Here's a group of 93rd PA men also wearing the modified jackets. A couple with the "Veteran volunteers" half chevron on the sleeves. They also wear custom slouch hats and slow crowned kepis ("McClellan caps" as the Union soldiers called them) in lieu of the army forage cap. One with a corps badge insignia on his jacket breast.
the veteran volunteer half-chevron was red and blue worsted braid.
3/4ths of the men of the 93rd reenlisted as "Veteran Volunteers" in February, 1864, and went home for a 30 day furlough, including a parade, etc. From that date the regiment was the "93rd Pennsylvania Veteran Volunteers" etc.
Here's another Union soldier of an unknown unit of the Sixth Corps, also wearing an infantry jacket, with veteran volunteer stripes, and a metal corps badge pinned to the breast.
A veteran of the 5th Wisconsin, with the Sixth Corps' first division, noted later they drew new caps prior to the Grand Review at Washington at the end of May, 1865...