Does anyone know what this patch is that my friend found?

A friend of mine found this patch in his house, and we're pretty sure it's WWII. I looked for WWI, Vietnam and Korea matches but I couldn't find anything.

Thanks, Ace_1 244​

 

"The shoulder sleeve insignia was approved for the War Department Overhead on July 30, 1941. It was redesignated for Headquarters, Services of Supply on March 27, 1942; redesignated as Army Service Force on March 12, 1943; redesignated Technical and Administrative Services on June 11, 1946; and redesignated as DA Staff Support on October 8, 1969"--The Institute of Heraldry.

Looks to be post-ww2.

The standard color version was red background, white cloud, & blue star.

 

Thank you!!