To test Apple Pay on your sandbox site, you'll need to use the Apple Pay Sandbox. Getting it setup takes just a few minutes and below are the steps you have to follow:
If you don't have one already, create an Apple Developer account.
Log into iTunes Connect.
Select Users and Roles, then select the Sandbox Testers link at the top of the page.
Next to "Testers", click ⊕ to create a new test user. Fill out the page, taking note of the email and password you used, and click Save on the upper right.
On your test iOS device, open the Settings app and tap iCloud. If you're signed in, tap Sign Out at the bottom.
Log in using the new test credentials you just created.
Tap Back to return to the first page of Settings, then tap Wallet & Apple Pay.
Tap Add Credit or Debit Card, then when prompted to photograph your card tap Enter Card Details Manually.
Enter 4761 1200 1000 0492, expiration 11/2022, CVV 533 (this is a test Visa card; for more test cards see the Apple Pay Sandbox Guide).