The Collaborative International Dictionary of English v.0.48:

Sheriffalty \Sher"iff*al*ty\, Sheriffdom \Sher"iff*dom\,
Sheriffry \Sher"iff*ry\, Sheriffship \Sher"iff*ship\,
Sheriffwick \Sher"iff*wick\, n.
   The office or jurisdiction of sheriff. See Shrievalty.
   [1913 Webster]

Bouvier's Law Dictionary, Revised 6th Ed (1856):

SHERIFFALTY. The office of sheriff, the time during which a sheriff is to
remain in office.