There are various ways of recording information in a double-entry system. There is no such thing as a right or wrong way. You need to figure out the best way that works for you and makes sense. The only requirement is that whenever you debit any account you also need to credit an account by the same amount to keep things in balance.
The ledger provide a picture of the financial state of your business. But it is up to you to decide how you want to paint the picture.
If you receive cash then you can debit the Cash On Hand account to indicate that you now have additional cash. If you receive a cheque which you pay into your bank account you should probably debit the Bank account to indicate that you now have extra money in the bank.
The matching credit should be made to an account that indicates where the money came from or the reason you received the money. In your case because it is income it makes sense to credit an income account (Fees Charged or Sales.)
You are right that Accounts Receivable seems inappropriate if you have already received the money. Accounts Receivable makes more sense for money that has not been received and is still owing.
Accounts Receivable is an asset account the same as Cash On Hand or Bank. In this situation you should debit the Accounts Receivable account with the amount that is owed and credit the income account (Fees Charged or Sales.)
You may also wish to create separate Accounts Receivable accounts for each of your clients that owe you money rather than combining these in a single account. This way you will be able to see by looking at the Balance Sheet who owes you money.