Do you need wifi or cellular connectivity to use Apple Pay

Apple Pay in and of itself does not require internet access.

Payments in physical stores are done through near field communications, i.e RF (radio frequencies) to connect with the payment terminals not wifi or cellular.

Apple Pay within Apps may require internet access to complete payment and access the paid-for content though.

Apple Pay through websites, will require internet access to view the website and process the payment there.

Using Apple Pay in stores, and within apps and websites - Apple Support