This is a photograph of my grandfather... his DD214 shows his last unit as Co C 52d AIB APO 221
The patch looks like its from the 52nd Armored Infantry Battalion, matching the " Co C 52d AIB" from the papers.
It was redesignated for the 52d Armored Infantry Regiment on 29 September 1942. The insignia was redesignated for the 52d Armored Infantry Battalion on 6 January 1944. It was redesignated for the 52d Infantry Regiment on 31 October 1958. […]
After the armistice, the six-point Red Star was adopted as the division insignia on 19 November 1918. This six-point Red Star became a part of the 52d Infantry's crest to mark the regiment's first combat with the 6th Division.
Its insignia as used on the shoulder patch is a just six-pointed star.
Thanks to the excellent eyes of user @Andrew, we also have a good estimate on the insignia on the cap and shoulder strap :
The cap badge seems to match the 20th Infantry Regiment, which was assigned to 6th Infantry Division until 1956 - and 6th ID would have had the same star badge. The division was a training unit at the time - is it possible he was there before being sent to 52nd AIB, and this was taken then?
And for completeness, user @Schwern notes that the data on the DD214
"Co C 52d AIB APO 221" is Company C, 52nd Armored Infantry Battalion, Army Post Office 221. The date would be useful. Note that your grandfather's company was involved in saving some 9th Armored tankers near Limburg.