A quick googley suggests that "The drop of York" referred to falling through the trapdoor on the gallows at York. The phrase could therefore be used to convey confidence in an assertion, i.e., "Hang me if I'm wrong!".
I have no idea, however, whether this is right or not but I wouldn't wanna do the Newgate Hornpipe for it.
My late father, a Yorkshireman as am I, asserted that it referred to the height of the central tower of York Minster. That the preposition was so preposterous that if found to be correct, the speaker could survive such a fall.