"by payment" is correct and usable in written English.
You can use it to describe how someone pays for something. For example: "The purchase was made by payment of cash."
He continues to be frustrated by payment denials.
Bitcoin to be accepted by payment service Stripe.
Rationing by payment may offend tradition, but rationing by chaos is cruel.
Big people, you know, somebody who has money, do it by payment.
Blood feuds occurred between segments and were settled by payment of blood money.
They are collections that have been built up over centuries by payment largely from the public purse.
Thus, the costs of hospital operation are covered infrequently by payments made directly by patients.
SINTEF is financed by the state and by payments for its services.
Sometimes they were turned back by defenses but more often by payments of tribute.
Journalism is also venal, shaped by payments from officials and businessmen.
American officials say they believe that the Hungarian and Czech governments were influenced by payments.
