How can I manage recurring payments in my app?

We are trying to create a shopify app that lets users develop a mobile app for their shopify stores. There will be different subscription plans in the shopify app for the users. We will be integrating shopify payment gateway/API for the payments for the subscription.Is there an option in shopify that handles the monthly/annual subscription payments that automatically pays the bill monthly/annually from the subscribers through their credit cards or other payment methods.

Shopify allows different pricing models for the app. If you want to bill the user monthly/anually you can implement a recurring charge API. In graphql API Shopify allows you can charge users both annually and monthly. However, if you are using REST Admin API you can only implement a monthly recurring charge. Once the user installed your app and if you have any trial period then users are automatically charged once the trial period ended and those charges are billed from the payments method user selected during approving your pricing plan.
You can find the implementation in the below documentation.
appSubscriptionCreate