Hi,
If you want to integrate third-party payment gateway or payment API and you dont have the payment API plugin to install into woocommerce then you are at the right place.
I will create a fully custom payment plugin for your woocommerce store using your payment API.
You can use this custom plugin on your woocommerce checkout page.
The custom plugin will have a Setting/Configuration page under woocommerce payment tab in woocommerc payment section.
On checkout page there will be an option to select the payment plugin and users will fill in their payment details and complete the checkout process.
Please contact me before ordering this gig. You need to share your payment API documentation.