Can't install Kali on a USB 3.0 SSD

I bought a USB 3.0 SSD to install kali on it for a high performant exteal boot setup. Unfortunately, I can't select my USB SSD in the installation process. I tried it on my laptop, but also via a VM. Both without success.
I tried different BIOS options on my laptop but it didn't make any difference. In the past I installed KALI on a USB 3.0 stick without problems (installation where I booted from a usb stick and installed kali on another usb stick).
I really have no clue what is causing the problem with the SSD. Is there any superuser with experience in this field? Thanks!