‘This family is originally of Norman extraction and was anciently called De La Montagne. In the reign of King Edward III, its members were styled Hill, alias De La Montagne; but in succeeding ages, they were known by the name of Hill only.
Sir Moyses Hill, Knt. (descended from the family of Hill, of Devonshire, two members of which were judges of England at the beginning of the 15th century, and one lord mayor of London, anno 1484), went over to Ireland as a military officer, with the Earl of Essex, in 1573, to suppress O’Neill’s rebellion; and was subsequently appointed governor of Olderfleet Castle, an important fortress at the period, as it protected the harbour of Larne from the invasion of the Scots. Sir Moyses represented the county of Antrim in the parliament of 1613, and having distinguished himself during a long life, both as a soldier and a magistrate, died in February 1629-30, and was succeeded by his elder son Peter Hill esq but we pass to his younger son Arthur who eventually inherited the estates on the demise of Peter’s only son Francis Hill esq of Hill Hall, without male issue.
The said Arthur Hill esq of Hillsborough, was colonel of a regiment in the service of King Charles I, and he sate in parliament under the usurpation of Cromwell, as well as after the Restoration, when he was sworn of the privy council…’
From A General and Heraldic Dictionary of the Peerage and Baronetage of the British Empire by John Burke, Esq. (1833)

‘Hillsborough: This place, originally called Cromlyn, derived its present name from a castle erected by Sir Arthur Hill in the reign of Chas. I, which at the time of the Restoration, was made a royal fortress by Chas. II, who made Sir Arthur and his heirs hereditary constables, with twenty warders and a well-appointed garrison. The castle if of great strength and is defended by four bastions commanding the road from Dublin to Belfast and Carrickfergus; it is still kept up as a royal garrison under the hereditary constableship of the present Marquess of Downshire, a descendant of the founder, and is also used as an armory for the yeomanry.’
From A Topographical Dictionary of Ireland by Samuel Lewis (1837) 

‘Colonel Hill, having built within a few years, at his own charge, and upon his own lands, during the rebellion, for the encouragement of an English plantation and security of the country, a considerable place of strength, called Hillsborough fortified with four bastions, or flankers, commanding the chief roads in the county of Down leading from Dublin to Belfast and Carrickfergus; His Majesty was pleased to consider that the surprise thereof, upon any insurrection, might prove very prejudicial to his service, and how much it would conduce to His Majesty’s service and the safety of the country that a guard should be placed in that fort for the security thereof; he therefore granted a patent at Westminster for erecting it into a royal garrison by the name of Hillsborough Fort, with a Constable and officers to command it, to be called and known by the name of Constable of Hillsborough Fort, and twenty warders to be nominated and chosen by him; the Constable to have an allowance of 3s. 2d. a day and the warders 6d. each; and this office was granted to him, his heirs and assigns, for ever.’
From Historical Notices of Old Belfast and its Vicinity; A Selection from the Mss. collected by William Pinkerton, Edited with notes by Robert M Young (1896)