Has anyone seen this patch used for APP before? It's listed on eBay as a APP STATE patch.

Never. Gotta be WVA

I bought my first App "logo" item in the bookstore in '61 while still a high school senior. There were quite a few shirt and windbreaker jacket options with a Yosef design very similar to the one shown in your post in stock and on display for sale. They were all screen-printed. No embroidered patches were available, as I recall.

Here's my take fwiw...
1. The eBay embroidery appears to me to be gold on black. An authentic WVU item should have been fabricated in gold on navy.
2. This may, indeed, be someone's attempt to market a "back in the day App Yosef" but the embroidery is way, way too sophisticated in fine detail to have been done on machines in use 50 or 60 years ago. This looks to me like something produced recently on a sophisticated digital embroidery machine.

Grab the quarter and run!

So i did some checking:
8 colleges/Unis have Mountaineers as a mascot
Appalachian State University. Mountaineers.
Berea College. Mountaineers.
Eastern Oklahoma State College. Mountaineers.
Eastern Oregon University. Mountaineers.
Mansfield University of Pennsylvania. Mountaineers.
Mount Saint Mary's University. ...
Southern Vermont College. ...
University of West Virginia-Morgantown.

We are the only one with Black and gold as our colors but I never saw that patch before

Never seen that logo for WVU - in my lifetime they have always used the Mountaineer with the coonskin hat and leather clothing and long rifle ---

Could be a high school patch.

"I've got a buddy that specializes in vintage patches. Let me give him a call to see what this things worth."

It seems familiar ....