1590s, "one who is the offspring of a European and a black African," from Spanish or Portuguese mulato "of mixed breed," literally "young mule," from mulo "mule," from Latin mulus (fem. mula) "mule" (see mule (n.1)); possibly in reference to hybrid origin of mules (compare Greek hēmi-onos "a mule," literally "a half-ass;" as an adjective, "one of mixed race"). As an adjective from 1670s. Fem. mulatta is attested from 1620s; mulattress from 1805.

American culture, even in its most rigidly segregated precincts, is patently and irrevocably composite. It is, regardless of all the hysterical protestations of those who would have it otherwise, incontestibly mulatto. Indeed, for all their traditional antagonisms and obvious differences, the so-called black and so-called white people of the United States resemble nobody else in the world so much as they resemble each other. [Albert Murray, "The Omni-Americans: Black Experience & American Culture," 1970]

Old English had sunderboren "born of disparate parents."

"person of mixed blood in America and Asia," 1748, perhaps from Spanish zambo "bandy-legged," which is probably from Latin scambus "bow-legged," from Greek skambos "bow-legged, crooked, bent." The word was used variously in different regions to indicate some mixture of African, European, and Indian blood; common senses were "child of black and Indian parentage" and "offspring of a black and a mulatto."

by 1886 in American English in reference to a type of hound bred in the South, with a red or red and tan coat, used especially to hunt raccoons and fugitives. The name probably has some connection to the term Redbone as used in 19c. southern U.S. to denote a mulatto or mixed-race culture.

The Redbone is one of the old-time strains; confined exclusively to the Southern States. The "native" Birdsong, Georgia, Virginia, and Kentucky Hounds were undoubtedly the Redbone strain before the introduction of the various crosses previously mentioned. They were a slow, painstaking Hound, with superior nose and splendid mouth, without speed. [Gen. Roger D. Williams, "The American Foxhound," in "Dogs," New York: 1907]

by 1781, an alteration (by influence of words in quadr-) of quarteroon (1707), "offspring of a white and a mulatto," from Spanish cuarteron (used chiefly of the offspring of a European and a mestizo), literally "one who has a fourth" (Negro blood), from cuarto "fourth," from Latin quartus "the fourth, fourth part," which is related to quattuor "four" (from PIE root *kwetwer- "four").

So called because he or she has one quarter African blood. There also was some use in 19c. of quintroon (from Spanish quinteron) "one who is fifth in descent from a Negro; one who has one-sixteenth Negro blood." OED lists quarter-caste as an Australian and New Zealand term for a person whose ancestry is one-quarter Aboriginal or Maori and 3/4 white (1948).

"'white' person, person of European descent," 1828, also whity, from white (adj.) + -y (2) and -y (3). Earlier as an adjective, and Whitey-brown was a 19c. descriptive color name, used to describe, among other things, mulatto skin.

Negro troops doing provost duty in Norfolk; keeping the white people in order. On a visit to Norfolk one can see white Southerners, arrested for sundry misdemeanors, working on the public streets, under negro guards. ... It is quite a change to see, in Norfolk, negroes forcing white men to work, at the point of the bayonet; calling out to them: "No loaf'n dar!" "Move quicker, Sah!" "Hurry up dar, Old Whitey!" and similar orders. Tables turned! [diary of Lieut. S. Millett Thompson, 13th New Hampshire Volunteer regiment, U.S. Army, Jan. 25, 1864; diary published 1888 by Houghton, Mifflin & Co.]