Which side of a receivables ledger control account is cash refund to customers?

If you are having to refund a customer money from an account receivable that means that

1. They overpaid on their account (or)

2. An entry error was made and they were over charged.

For example 1. Say Customer X paid you $500 on their account but only owed you $50. The original entry is going to give their AR a (credit balance) of $450. Because AR is an account receivable it maintains a Debit balance. To correct this and your company plans on paying them cash back (issuing a check), you will Issue the check for $450 and credit your cash account and debit their AR account. This entry will not effect revenue as it was an over payment and not actually recorded as Income.

If it's just an entry error, then simply correct it with an adjusting entry. Since the original entry is recorded as AR (debit) and Revenue (credit), reverse the entries for the adjustment amount noting why the adjusting entry was made. Since this was an entry error more than likely Income (revenue) was entered wrong as well.