DLAN-Subscription

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It's normal to create a Subscription for a customer, then fulfill their first Payment by a PaymentIntent. You don't need SetupIntent, it's for different purpose

You also can use Stripe Billing Portal to let your customer change their Paymentmethod for their Subscription, instead of building a button yourself

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Okay so I can use another payment intent to change the card? Would I pull the client secret from the current subscription, instead of creating a new subscription?

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For each time of charge you would want different PaymentIntent, hence different client secret (client secret is created per PaymentIntent) But that's how you create separate Charge with the Subscription. The Subscription itself will automatically create an Invoice, then a PaymentIntent on renewal billing date