Do you mean to fetch payments made against orders with a specific order type (for example, all payments made on "to go" or "dine in" orders) or are you trying to just fetch a single payment and get the order type of the order the payment was made on?
here is query example what am tying to fetch you will get this...
{baseUrl}/v3/merchants/{merchantId}/payments?expand=lineItemPayments&filter=orderType.id={orderTypeId)
{baseUrl}/v3/merchants/{merchantId}/order_types
<em>{baseUrl}/v3/merchants/{merchantId}/orders?filter=orderType={orderTypeId}&expand=orderType,payments</em>
1 Person is following this question.