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How App Store and iTunes Store purchases are billed - https://support.apple.com/HT201359

"Which payment method is charged?

When you buy items or pay for subscriptions, Apple attempts to charge your payment methods in this order:

1. Apple attempts to use your Apple ID balance to cover the full amount.

2. If you don't have Apple ID balance or you don't have enough to cover the full amount, Apple attempts to charge your primary payment method. The primary payment method is at the top of the list in Settings on your iPhone. You can control which payment method is at the top of the list.

3. If there's a problem with the primary payment method, or if the primary payment method can't be charged for the full remaining amount, Apple attempts to charge your other payment methods in order from top to bottom. If none of them can be charged, Apple may try again.

The order is automatic. The only way to control a chage to go to a particular card is to ensure you have no Apple ID balance, so a card gets charged, and also to move your desired card to the primary payment method position.

Since Apple (and people asking questions) apparently prefers I don't explain things then I will just say:

No, in practical terms you can't do it the way you wish.

You could finesse it to only charge certain things to a particular card by using the method I outlined but it would take some pretty fine timing in changing the primary payment method and control of whether or not you have any Apple ID balance. You could do it but it would not be easy (and I didn't claim it would be!)

No way not to use your Apple account. All subscriptions started on an Apple device, will by definition use your Apple account and its associated payment method.

You can as mentioned change the primary payment method on your Apple ID to something else if you need to, ut then all the charges from the iTunes Store, App Store and iCloud will use that payment method.

Thank you. (I had an issue with Apple and a person posting a question earlier and it ruffled my feathers. You have restored my confidence in humanity. ;-D )