How to Submit a Payment for an open Invoice in Apex?

Our use case is as follows:

1. Customer goes to our website, enters credit card information and signs up for the product.
2. Order and Contract is created and activated
3. Invoice is created and posted.

Now we need to make a payment with the credit card entered for the open Invoice. Is it possible to make payment in this case for the Invoice similar to what payment scheduler does(Payment transaction, allocation and etc..) in Apex? Is there a API to make this process easier?

OR

Can we create a payment scheduler so that it targets only this particular Invoice? I am aware of the Payment Batch field on Payment scheduler and it targets all Invoices matching with Payment Batch. I am looking for a way to match only single Invoice.