A territory (principality, province...) ruled/administered by a count.(noun)
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Use "countship" in a sentence
"We were in partnership with a Florentine, well known in all the Courts of Europe, the Count Alessandro Pippi, as skilful a player as ever was seen; but he turned out a sad knave latterly, and I have discovered that his countship was a mere imposture."
"“Aye, feel free to wake his countship up,” Deryn said."
"His countship was offering her, a lowly middy, a cup of tea?"