Sherbet is the standard spelling of the frozen dessert made primarily of fruit juice, water, and sugar. The misspelled sherbert, which results from a common mispronunciation (sher-bert instead of sher-bit), appears often enough to have earned a spot in some dictionaries as a secondary spelling, but it is still not as widely accepted as sherbet, which more closely resembles the Turkish and Persian words from which the English term is derived.
The word has been spelled many ways over the centuries. Zerbet, cerbet, shurbet, sherpet, sherbette, and sarbet, among others, are all found in the Oxford English Dictionary’s historical examples. Sherbert is also listed, and many instances of that spelling are also found in historical Google Books searches covering the 18th and 19th centuries. Sherbet became the unquestionably standard spelling by the middle 19th century, however, and since then only sherbert has given it any competition.
Sherbert appears only a fraction of the time in edited writing, as shown in this ngram graphing the use of sherbet and sherbert in English-language texts published from 1800 to 2000: