Apple Pay has no verification process. I suspect you’re referring to Apple Cash which is serviced by Green Dot Bank. Green Dot in compliance with federal banking regulations must positively identify their customers. These regulations are common known as KYC regulations (Known Your Customers).
The loop you’re experiencing generally means they’re having an issue identifying you or you’re not eligible for the service.
Apple plays no part in the verification process and all results are only known to Green Dot Bank. Apple is not a bank and offers Apple Cash as a service to Apple owners and users. The please contact an Apple Cash specialist at Green Dot Bank for further assistance.
Contact Green Dot Bank:
by calling (877) 233-8552,
by mail for disputes at P.O. Box 9, West Chester, Ohio,
by mail for general customer service at P.O. Box 1070, West Chester, Ohio 45071,
visit www.greendot.com
https://applecash.greendot.com/termsconditions/