1610s, "native or inhabitant of Malta;" 1797 (adj.) "of or pertaining to Malta, from Malta + -ese. Maltese cross is from 1754 (earlier Malta cross, 1650s), so called because it was worn by the Knights of Malta. Maltese cat is attested from 1830: any cat with fur completely or primarily gray or blue, supposedly a common trait among cats on the island, but the breeds that noted for this coloring are not associated with Malta. As a type of very small dog, known since ancient times in the Mediterranean, it is attested in English by 1803.
Strabo informs us, that "there is a town in Pachynus, a promontory of Sicily, (called Meleta,) from whence are transported many fine little dogs, called Melitae Canes. They were accounted the jewels of women; but now the said town is possessed by fishermen, and there is no such reckoning made of those tender little dogs, which are not bigger than common ferrets or weasels; yet are they not small in understanding, nor unstable in their love to men, for which cause they are also nourished tenderly for pleasure." [Capt. Thomas Brown, "Biographical Sketches and Authentic Anecdotes of Dogs," Edinburgh, 1829]