How to assign a payment on account from cashbook to a supplier - seems to show it as an additional expense on supplier account instead of payment

Thank you for posting, @tusharv.

In QuickBooks Online, you can use Bill for bills that'll be paid later, then Pay bills to clear the bill and generate the cheque. However, you can use  Cheque and Expense if the expense was paid at the same time. 

You can record an expense as a Cheque if you need to print a cheque and Expense if you've paid it through card. 

To know more about this, check the following article: What is the difference between bills, cheques, and expenses?. 

Let me know if you still have follow-up questions in recording your transactions. I'm always here to assist. Have a wonderful day!