Sicily is an autonomous region of Italy, not a sovereign state. It has never had its own currency. Italy adopted the euro on January 1, 1999 (electronic) and January 1, 2002 (cash), replacing the Italian lira.
Questions about "Sicily's currency" sometimes arise from misunderstanding its autonomous status (it has its own parliament and certain legislative powers) or confusion with microstates like Vatican City/San Marino (which use euro by agreement). Sicily is simply part of Italy's monetary union.