It's possible you might be thinking of a related term, "barysphere", which is a term sometimes used in geology. However, barysphere is not a standard term either.
It's important to note that the prefix "baro-" often refers to pressure, as in "barometer." However, "barysphere" is sometimes used (though not widely accepted) to describe the deepest part of the Earth's interior, specifically the core.
If you have more context for where you encountered the term "barosphere," it may help clarify what it actually refers to.
