What are the organisms still alive that display some of the earliest vertebrate evolutionary characteristics?

Hagfish and Lamprey

Explanation:

Vertebrates are the organism which posses vertebral column or the spinal cord in their skeleton.

The earliest vertebrates had the cranial structures or head but they lacked the vertebral columns and the jaws. These earliest vertebrates lived around 500 to 600 million years ago.

The earliest vertebrates which lacked the vertebral columns and are still alive are the Hagfish and the sea lampreys. These are considered the earliest vertebrates as they lacked the jaws.

These jawless fish are the ancestors of the cartilaginous and bony fish which later developed into amphibians and other groups of animals.

Thus, Hagfish and Lamprey are the earliest vertebrates.