Here are some books you might look at. Also, be sure to mine the footnotes for references to the journal literature.
Anything written by Anthony Luttrell, who is the main authority on the Hospitallers
Jurgen Sarnowsky, ed., Mendicants, Military Orders and Regionalism in Medieval Europe (Aldershot, 1999)
Jonathan Riley-Smith, Hospitallers: The History of the Order of St. John (Hambledon Press, 1999)
Kenneth M. Setton, The Papacy and the Levant (American Philosophical Society, 1984)
Norman Housley, The Later Crusades 1274-1580: From Lyons to Alcazar (Oxford University Press, 1992)
Norman Housley, Crusading in the Fifteenth Century (Palgrave Macmillan, 2004)
Helen Nicholson, The Knights Hospitaller (Boydell, 2001)
Norman Housley, Documents on the Later Crusades, 1274-1580 (Saint Martin's, 1996)
Francesco Balbi, The Siege of Malta, 1565. Translated by Henri Alexander Balbi (Bagsvaerd, 1961)
Desmond Seward, The Monks of War (Penguin, 1995)
Anything by Ernle Bradford, although most of his work is more literary than historical