You can absolutely apply to become a third party payment provider - the first step in this process would be to become a Shopify Partner, are you currently part of our Partner programme? The minimum requirement which must be met in order to apply include:
They need to implement the ability for a merchant to charge, refund, and process test transactions.
They need to be 3DS compliance if they’re processing credit card payments in specific countries.
Idempotency: To provide a consistent customer experience, payments apps must implement idempotency.
Retry policy: In case of network errors, payments apps must retry their requests according to the retry policy.
Mutual TLS (mTLS): Authentication must be implemented to guarantee that traffic is secure and trusted in both directions between Shopify and your payments app. This authentication allows your app to confirm if an upstream request has originated from Shopify. Payments apps must use the Shopify CA certificate for verification.
Rate limiting: Your app’s GraphQL requests are rate limited according to the rate limiting guidelines.
API Versioning: Partners must implement a supported version of Shopify’s Payments Apps APIs. Partners can configure the API version that their payments app will use to receive requests from Shopify. Partners must use the same API version for sending GraphQL requests. API versions are updated in accordance with Shopify’s general API versioning timelines.
3-D Secure: If you offer credit card payment methods in a country where 3-D Secure authentication is mandated, then you must support 3-D Secure authentication.
GDPR: You need to implement GDPR webhooks.
App extension configuration change approvals: To provide a positive buyer experience for customers, your app extension configuration changes must be approved by Shopify.
For full requirements and definitions of all the terms above, you can read the requirements and all other information in full here. An outline of what the steps for application of your app can be found via this link, this image also gives a brief breakdown of what the process looks like:
I have been speaking to the merchant support team who have been very helpful and are currently in the process of finding my application as there doesn’t appear to be a record of it from my understanding!