Solved.
Turns out that this a not well known issue of macOS. For usb external usb drive, sometimes usb-c port of a Mac won't work on booting macOS.
My drive is a usb 3.1 type-c drive. I connect it with my Mac mini over a usb c-c line. That cause the macOS issue. The solution is to change a c-a line. Some how, in that way, and a reinstallation of macOS, everything works.
Conclusion:
1. For a Mac with usb-a and usb-c ports use usb-a to boot macOS in external disk.
2. For a Mac with usb-c only ports, if you encounter the same issue, the only solution is to use a thunderbolt 3 drive.
However, above is for usb 3.1/3.2 10Gbps drive. I have not tested with drive that works with usb4/thunderbold3/usb3.1.