Try erasing and formatting the entire disk/SSD. Also, if you are running High Sierra (OS 10.13.x, with OS 10.13.5 being the latest version), it might be better to format that SSD as APFS.
I have 2 external Samsung 850 Pro 512 gig SSDs enclosed in nice, slim Orico enclosures. Each of those SSDs has 3 partitions. 2 of the partitions are for my SuperDuper! backups for each of my Macs running OS 10.13.x (now OS 10.13.5), and those partitions are formatted as APFS. The third partition contains miscellaneous "stuff" (old tax returns, movies, TV series, photos, etc.), and it is formatted as MacOS Extended (Journaled), with GUID as the scheme. All of that works very well for me.
And of course, given that SuperDuper! makes a bootable backup/clone, I can boot either of my Macs from either of those partitions.