Said to be derived from St. Kilian, whose image was
stamped on the “shillings” of Würzburg. Of course this etymology is of
no value. (Anglo-Saxon, scylling or scilling, a
shilling.)
According to Skeat, from the verb scylan (to divide). The
coin was originally made with a deeply-indented cross, and could
easily be divided into halves or quarters.
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894