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In appeals from final judgments for child custody, you have 15 days from the date shown in the clerk's certificate of distribution at the bottom of the final judgment, decree or decision to file a Notice of Appeal.
Generally speaking, the judge will set up a scheduling order for the custody case. By this time, anywhere from 3 weeks to a month has passed from the date of the filing of the petition to the first appearance, and anywhere from 2 weeks to a month for the date of the second appearance.