You were likely told that you wouldn't have a conviction on your record. Supervision is not considered by the courts to be a conviction, so if you completed it, you don't have a conviction on your record. However, you still have a record-namely, the arrest and the charges.
Section 5.2 of the Criminal Identification Act (20 ILCS 2630/5.2) allows qualifying arrests, supervisions and convictions to be either expunged or sealed. Only those individuals who have never been convicted of a criminal offense or municipal ordinance violation are
eligible to expunge records. If you have ever been convicted of a criminal offense or a municipal ordinance violation, your records may still be eligible for sealing, but you cannot expunge any records, regardless of the outcome of the individual case.
Using the written documentation you have is a good place to begin. Contact a local lawyer - many may give you a short free consultation - to discuss your specifics. Far too many variables exist in the short post you wrote for any further observation by me. Many attorneys have information posted here on Avvo.
You might find my Legal Guide helpful "How to Choose A Lawyer For You"
You might find my Legal Guide helpful " What Do I Tell My Lawyer"
No one can know what the record is in the case because online we cannot see your documents. You need a lawyer. Check with a lawyer in your locale to discuss more of the details.
Good luck to you. God bless. Best of luck to you.
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Unless your charge was amended from domestic battery to battery (or something else), you did not receive supervision since that is not an available sentence for domestic battery. Only supervision or a dismissal of the charge would be eligible to be expunged. If you got probation or conditional discharge then you have a conviction on your record that can never be expunged. The records from the Clerk of the Circuit Court will tell you what the disposition on your case was.