shopify payment API integration w a custom checkout page

Shopify Partner
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Is it possible to integrate the Shopify payment API on a custom site? I'd like to build a checkout page that will be custom developed and would like to use the Shopify payment for that checkout page? That page will be hosted externally. On the Shopify site, I am using Shopify payment and PayPal for the payment options.

For example, my checkout page will be hosted something like that-

Please help if is this something that is possible to integrate.