The message is confusing. Many have posted similar questions and I suggest you send feedback to Apple about it (I have). There is also no mention in any support documents what "verification" actually means. Feedback to: - http://www.apple.com/feedback/itunesapp.html
I am guessing it means they want you to verify your payment information is up to date.* See if this is what they want: Change or remove your payment information from your iTunes Store account (Apple ID) - https://support.apple.com/HT201266
and if it doesn't help then: iTunes [Store] Support - Use this form for assistance with account and billing, code redemption, or purchase questions - https://ssl.apple.com/emea/support/itunes/contact.html
* E.g., https://discussions.apple.com/thread/8311981?answerId=33131818022#33131818022
Alternatively set payment to none but you will ultimately need to resolve the payment problem.
Removing a credit card from an account - Change or remove your Apple ID payment information - https://support.apple.com/HT201266 - More information at: https://discussions.apple.com/thread/3251676?answerId=15891166022#15891166022
If you can‘t choose None when you edit your Apple ID payment information - https://support.apple.com/HT203905 - also make sure you don't have any active subscriptions, are set as the Family Organizer for a Family Sharing plan, or owe any money for past purchases.
You can only choose None when you set your payment method up from the iTunes Store, App Store, iBooks Store, or Mac App Store. None is not an option when you use the Apple ID account page to set your payment method.
Sign in with your Apple ID - https://support.apple.com/HT204053 - "When you sign in to the iTunes & App Store for the first time, you might need to add a credit card or other payment information to help secure your account." 20170919
iTunes [Store] Support - Use this form for assistance with account and billing, code redemption, or purchase questions - https://ssl.apple.com/emea/support/itunes/contact.html