Noun
The seigniory, dignity, or lordship of a marquis; the territory governed by a marquis.
Source: Webster's dictionaryMalta was elevated to a county and a marquisate, but its trade was now totally ruined, and for a considerable period of it remained solely a fortified garrison. Source: Internet
The dignity, rank or position of the title is referred to as a marquisate or marquessate. Source: Internet