how to log a payment via API ?

Context: I'm automating payments from an external payment processor

Via API, I was able successfully create an order, and a paid invoice under the order

in the invoice, I specified the amount paid ... but when I go into the order page and looked at the insights/total, the amount paid is not included in the total

after talking w/ the clickfunnels bot and support, we determined that its because no payment was logged (when I checked orders > payments, there is no corresponding entry there) ... how can I crate / log payment via API ?