I sent a payment to the wrong person

You can only cancel a payment if the person has not received it yet. Apple Cash should only be sent to people you know. Usually these people are in your Contacts and you would never need to enter the number manually in messages. To get the money back, you will need to ask that person for your money back. Apple Cash is a private transaction between two people and is similar to giving someone $20 on the street. This is detailed in the Support Article that details sending cash.

If you don't see Cancel Payment, the person has already accepted the payment. Try asking the recipient to send the money back to you instead.

Apple Cash person-to-person payments are like any other private transaction between two people, so only send and receive money with people you know. 

Send and receive money with Apple Cash - Apple Support

Assuming you used Messages to send the payment from Apple Cash, If the person has not accepted the payment you can cancel it by following the steps in the link below.

click here ➜ Send and receive money with Apple Cash - Cancel or Dispute a payment - Apple Support

If the money has already been accepted, then the only way to get it back is to ask the person you sent it to to return it.

Apple Cash is a service that’s administered by Green Dot Bank. Contact an Apple Cash Specialist at Green Dot Bank by calling (877)-233-8552 or by calling 1-800-MY-APPLE

https://applecash.greendot.com/termsconditions/