I don't know Illinois court rules but, in general, an appeal is withdrawn by communicating with the appellate court, not the court of origin. But you can start with the Civil Appeals Desk. They may direct you to the clerk of the appellate court , whom you can ask how to withdraw a pro se appeal that has not been perfected.
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I agree with my colleague's very sensible advice. And I am not licensed in Illinois. But I also think you probably can't go wrong by just filing a simple withdrawal of the appeal with the appellate court. I doubt a specific form is required, although your jurisdiction may have one available. Something like, "Appellant, Name, hereby gives notice of the voluntary dismissal of this appeal. Respectfully submitted, Name." Good luck.
Illinois Supreme Court Rule 309 provides that an appeal can be dismissed by the trial court before the record is filed in the reviewing court, which is your situation, either on motion of the party taking the appeal or by stipulation of the parties. In other words, you will need to get your motion or stipulation to dismiss before the trial judge to get the appropriate order entered. It should be no problem. Courts are always happy to see a case voluntarily dismissed. I don't know how much the clerk will be able to help you. You can ask.