The Gatehouse website record of a licence to crenellate for Quarr Abbey granted on 1365 Oct 24

Willielmus, Abbas de Quarrera et Conventus ejusdem loci in proprio ipsorum Abbatis et Conventus infra dictam Insulam tam in loco vocato Fisshehous super costeram maris situato quam alibi ubi eis melius expedire videbitur diversas placeas terrae tantas quantas et de quo procinctu eis placuerit muro de petra et calce includere, firmare et kernellare et castra vel fortalicia inde facere ... locum vocatum Fisshehous et diversas placeas terrae ... Quarrera, Insula Vecta. (Turner and Parker)
Licence for William, abbot of Quarr, in the Isle of Wight, and the convent of the same place, in the lifetime of the said William, to enclose with a wall and crenellate as many plots of land and of such precinct as they please on their own soil in the island, as well in the place called "Fisshehous" on the coast as elsewhere where it shall be expedient, and make castles of fortalices of these. By p.s. (CPR)

{1366} June 12. Westminster. Whereas the king lately granted licence for William, abbot, and the convent of Quarre in the Isle of Wight, to enclose and crenellate divers plots of land on their own soil and make castles and fortalices thereon in a place called ' Fisshehous ' on the sea coast and elsewhere in the island; he has now learned on the abbot's behalf that, whereas he has caused certain fortalices to be constructed at Fisshehous and at the abbot's mill and elsewhere in the island by virtue of the said licence, certain men of those parts, are scheming to hinder those works and often set themselves to lay low and destroy the works begun by the abbot at his mill; the king has therefore taken the abbot, monks and fellow-brethren, and the workmen and works of the abbey into his special protection, and has appointed Richard de Pembrugg and Theobald de Gorges, and deputies whom at the request of the abbot they shall appoint, to survey the works, maintain and defend the abbot, monks, workmen and works, and arrest all contrariants, during pleasure. (CPR)

Comments

On June 12 1366 the Calendar of Patent Rolls records fortalices are being constructed at Fisshehous and at the abbot's mill and elsewhere but that certain men are scheming to hinder the works and destroy those at the abbot's mill. The king grants special protection and the power to arrest contrariants.
The position of these forts suggests that genuine coastal fortifications, protecting the Solent, as well the Abbot's lands on the Isle of Wight, were intended and built. Presumably the stated reason for such fortifications was French raids but the interference from local people raises questions as to what concerns local people would have had about such fortifications.
It was common for the Abbot of the Quarr Abbey to be appointed Warden or Lord of the Island.

In 1366 Edward III. granted the abbey licence to crenelate as a safeguard against foreign invasion, and about the same time letters patent were issued that all wine ships belonging to the community should come and go free of duty. The abbots of Quarr held a distinguished position in the Isle of Wight. When a commission of array was issued in April, 1380, on information of an intended invasion by France and Spain, the abbot of Quarr headed the list of eight gentlemen nominated by the Crown, preceding even Sir Thomas de Beauchamp, the governor of Carisbrooke castle. (VCH)

Original source is;

Lyte, H.C. Maxwell (ed), 1912, Calendar of Patent Rolls (1364-67) p. 168 online copy
ibid p. 253 online copy

(In fact, the original source given is usually a transcription/translation of what are precious medieval documents not readily availably. It should be noted that these transcription/translations often date to the nineteenth or early twentieth centuries and that unwitting bias of transcribers may affect the translation. Care should also be taken to avoid giving modern meaning to the medieval use of certain stock words and terms. Licentia is best translated as 'freedom to' not 'permission'.)

Significant later sources are;

King, D.J.C., 1983, Castellarium Anglicanum (London: Kraus) Vol. 1 p. 200n61
Coulson, C., 1982, 'Hierarchism in Conventual Crenellation' Medieval Archaeology Vol. 26 p. 94 online copy
Turner, T.H. and Parker, J.H., 1859, Some account of Domestic Architecture in England (Oxford) Vol. 3 part 2 p. 416 online copy