What 68-pin connector is this on my 2.5" solid state drive?

It's a U.2 interface, formerly known as SFF-8639.

U.2 can be used for SATA Express, SAS, or Enterprise PCIe. As far as I can see, the 2.5" U.2 version of the Samsung PM983 is only available as PCIe. In this case, it'd be possible to adapt to M.2 (NVMe only) or a PCIe x4 card.

Per this table on the Samsung website, all PM983 drives use the PCIe Gen3 x4 interface which I believe is a data centre blade interface. I don't believe you can plug this into a desktop PC with a regular SATA style cable.

SAS (serial attached SCSI) in a form factor partially compatible with SATA

(SFF-8482)

https://en.wikipedia.org/wiki/Serial_Attached_SCSI

p.s. it is partially compatible w/ SATA in a sense that a SAS host can run a SATA disk, but not the other way round.