Earliest known appearance in print: 1880 (see Comments below).1
Earliest known appearance in print, attributed to Thomas Jefferson: 19832
Other attributions: Andrew Jackson; Mark Twain; G.K. Chesterton; W.C. Fields
Comments: We currently have no evidence to confirm that Thomas Jefferson ever said or wrote, "I have nothing but contempt for anyone who can spell a word only one way," or any variation thereof. Jefferson's recorded comments on the subject of spelling would suggest that his opinions ran counter to the quotation in question. For example, he wrote to his daughter in 1783, "Take care that you never spell a word wrong. Always before you write a word consider how it is spelt, and if you do not remember it, turn to a dictionary. It produces great praise to a lady to spell well."3 In 1813 he wrote to John Wilson, who had proposed a system of orthography reform for the English language, "the want of conformity between the combinations of letters, and the sounds they should represent increases to foreigners the difficulty of acquiring the language, occasions great loss of time to children in learning to read, and renders correct spelling rare but in those who read much."4
This saying and other similar variations have been attributed to numerous people, as well as appearing in print as an anonymous witticism. The Yale Book of Quotations traces its print origins back to at least 1880;5 Ralph Keyes, in The Quote Verifier, concludes that it is simply an "old gag."6
1. To establish the earliest appearance of this phrase in print, the following sources were searched for the phrase, "spell a word only one way": Google Books, Google Scholar, Amazon.com, Internet Archive, America's Historical Newspapers, American Broadsides and Ephemera Series I, Early American Imprints Series I and II, Eighteenth Century Collections Online, 19th Century U.S. Newspapers, American Periodicals Series Online, JSTOR.