How to verify Apple ID payment method?

Tap Continue and sign in to view 'your' billing information.

You need to -> Sign in to your Apple ID account page and edit / update your Apple ID details.

https://appleid.apple.com                                                     

On the Sidebar click Payment methods -> then tap Payments Methods and tap Manage payment method.

Or -> Add a payment method to your Apple ID

Add a payment method to your Apple ID – Apple Support (UK)

• If you want to change your card, you need to add first the new card, then remove the old card.
• or if you use your Apple ID balance, you need to set your Apple ID balance as your default payment.

If you update your payment method or add funds to your Apple ID balance, It would take about 1 to 3 business days in order to process.

If you're still unable to update your payment method, Contact Apple Support.