There wasn't much in terms of cases for the Orange Pi Zero 3 when I purchased it last year. I decided to take a stab at it myself. A total of 5x M3x6mm screws are optional, this is a pretty snug case, so only the one for the standoff is necessary in my opinion. The clearances are tight, otherwise the MicroSD card would be pretty much impossible to remove.

To install the board in the case, first install the standoff onto the hat/dev board on the side opposite of the connector. Angle the board into the case, with the ethernet and USB ports pushed through the front like pictured below, and then give the back a gentle push down, it should slide down and click into place. You may need to push out a bit on the back of the case where the USB port and audio jack are. Removal is the reverse, pushing on the back USB ports while gently pulling on the back to free the audio jack and it should pop out.

Check my other models if you need a smaller version without the changes to fit a hat.