Why are my payment methods being declined for free app downloads on iPhone?

You will need a valid payment method on file even to download free apps.

If you can’t download or update apps on your iPhone or iPad - Apple Support

If you have a previous payment that was unable to be processed due to the invalid payment method, that will need to be paid first.

If a message says 'billing problem with previous purchase' or 'verification required' - Apple Support

To see if you have any previous purchases that are pending, you can view your purchase history and the amount will be showing in red or listed as Pending.

View your purchase history for the App Store and other Apple media services - Apple Support

If your current payment method is not determined to be valid, you will need to add a payment method that is valid. A small pending charge may be seen to determine if the payment method is valid and will then be removed.

Add a payment method to your Apple Account - Apple Support

Please contact iTunes Support. They can help. You resolve this issue.

To contact iTunes Support, do this: 

1. Click on this link --> Choose your country or region - Official Apple Support  

2. Select your country

3. Select: Billing & Subscriptions

4. Select: Subscriptions & Purchases

5. Select: Update payment method

6. Select a chat session or a phone call.

Copied from iTunes support - Apple Community