Origin of the Yost and Jost surname:
by J. W. Diederich
The most widely used alphabet on earth is the one the Romans developed and took with them as they conquered the Western world.  The uppercase letters you're reading are the same ones the Romans were reading in 600 B.C.  Roman publishers developed the lowercase forms around A.D. 300.

The only changes since then came in medieval times, when printing began and typographers invented the "J" to represent the consonant value of "I" and "V" was divided into "U," "V" and "W."

The surname Yost is derived from Iost, a form of an old Christian name, Iodocus.   When Europeans began to adopt surnames, between the year 1000 and 1500, many unrelated people selected Iodocus or Iost, probably because that was the given name of their father.

Thus, Iost became Jost.  In America, Yost was gradually adopted as the spelling of the name Jost because the first letter of the name was pronounced like a "Y" as in Yes rather than like a "J" as in John.

Thus, there are many families named Jost and Yost and they are not necessarily related.