I have a an airport extreme and it does not recognize my ssd drive whenever you plug it in to the usb of my airport extreme. I was able to plug my hdd drive and it got recognized easily.

How is the SSD drive formatted?

Connect the drive directly to your Mac and the drive icon will appear on the desktop

Right-Click on the drive icon, then click on Get Info

Look for Format in the next window that appears

The USB port on the AirPort Extreme is compatible with drives that are formatted in Mac OS Extended (Journaled), also known as HFS+, or FAT32.

HFS+ is highly recommended. FAT 32 is not.

Also note that the USB port on the AirPort Extreme is underpowered, so the drive may not appear even if the hard drive is formatted correctly. In that case, you can try to use a powered USB hub with the SSD drive.

Finally, the port on the AirPort Extreme is an old USB 2.0 design. That means that it is going to be....S.....L....O.....W.