Hey there, Kyle. Welcome to the community!
I'm not really sure what you want to do here? As far as I know you can use an external drive just for backups on a PS4 (e.g. you can't install games and run them from it).
It sounds like you're talking about an external enclosure with external power, but with a SATA connection for the data instead of a USB? I must say, that I seriously doubt that such a thing exists. Anyways, oPn your S4 there's only one SATA connection for power and one for data, which means that they are being used by your internal drive so even if such a cable or enclosure exists, you'd still have no way to connect it to the console. I'd recommend that you upgrade your internal drive, by going for one with larger storage capacity: https://support.us.playstation.com/articles/en_US/KC_Article/Upgrade-PS4-HDD/
I might have misunderstood you about the enclosure, so excuse me if this is the case and please, do try to explain what you mean exactly.
Hope that helps.
Boogieman_WD