A prehistoric sea scorpion (Eurypterus Remipes) was designated the official state fossil of New York in 1984. Eurypterus Remipes is an extinct relative of the modern king crab and sea scorpion.

This creature lived over 400 million years ago during the Silurian Age and crawled along the bottom of the shallow, brackish sea then covering much of what is now New York state.

Eurypterids are very rare fossils worldwide - New York State is one of only a few places in the world where euryterids can be commonly found. See State Fossils & Dinosaurs for all 50 States.

Source:

New York State Emblems: NY State Library
Eurypterus remipes: Paleontological Research Institute
Invertebrate Paleonology Image Gallery: Yale University: Peabody Museum of Natural History

Links:

State Fossils & Dinosaurs: 50 States