About 3 3/8" tall, gold embroidery on black felt which is backed with a light fabric interfacing, I think for dress uniform. NOS or New, Old Surplus item, I don't think it was ever on a uniform but may have been in a vintage patch bin. Ideal for any WWII collection.
The original Administrative patch featured a "V" on an anchor but was changed to a Caduceus in 1935. They don't necessarily indicate medical, they have a broader meaning.