My Dad found this in Whitby a few months ago. I know it isn't much, but we keep everything we find in Whitby because we rarely get to go there. I found a few nice complete ammonites and bivalves, and my Dad found this.
Is it a negative ammonite fragment - maybe Dactyleoceras commune?
Not much to go one with your specimen but it probably is related to the Dactylioceras ammonite family.
Last year the lads had a walk on the beach under the 'Abbey" (east cliff) and just on the other side of the sea defences they found a water worn bone block, several good ammonites, many partial ammonites and some bivalves.
This venue is probably one of the easiest places to go to around the Whitby area with a chance of a decent fossil.
Just remember the tide times as I was once vertually cut off.