If the invoice has not been sent to your accounting system, then all you need to do is add a payment to the invoice, (see sample image below):
Open the invoice you wish to add a payment to, under the invoices tab in the right hand side
Scroll down on the invoice and click 'add payment'
Add the necessary details to your payment.
If the invoice has been sent to your accounting system, then there isn't any way to update the Paid Status of a Tradify Invoice from the accounting system currently.
Essentially once the invoice has been sent to your accounting system, Tradify leaves the debt collection process up to the accounting system from then on and does not monitor the paid status of the invoice any further.
If this is absolutely vital to your operation, then you could try altering the integration method to use Tradify's invoice numbering sequence, which will allow you to track and process the payments in Tradify and then send them to your accounting system when they are paid. However, the debt collection processes and payment allocation processes in accounting systems are far more comprehensive than they are in Tradify.