This Seagate Backup Plus Ultra Slim Seems to meet your requirements. Its slim, coming in at 9.6mm tall.

I tried finding an SSD solution for you, but nothing would fit in that form factor. If your willing to settle on 512GB, I would recommend the AngleBird SSD2go, it is smaller... and substantially faster than any HDD.

The Seagate drive is a USB 3.0, and the Anglefire is USB 3.1 Gen2 10Gbit/s.
These are my suggestions, I hope they help.

Seagate Backup Plus Slim 1TB Portable External Hard Drive for Mac USB 3.0 Seems to meet your requirements. Its slim, coming in at 9.6mm tall.

I tried finding an SSD solution for you, but nothing would fit in that form factor. If your willing to settle on 512GB, I would recommend the AngleBird SSD2go, it is smaller... and substantially faster than any HDD.

The Seagate drive is a USB 3.0, and the Anglefire is USB 3.1 Gen2 10Gbit/s.
These are my suggestions, I hope they help.