i imagine you've had time to research zelle while waiting for a
response to your post. if not, know that the banks are not
going to deal with you (nothing personal). the banks already
have an app to do what it is you are looking to do. there are
a couple "integrators" out there which, in exchange for a
monthly fee will let you interface with their (approved) platform.
possibly via a REST-ful api. you transmit the request to the
integrator, and it passes it on to a member bank (presumably,
the bank which has agreed to work with the integrator).
this is not unlike handling credit card transactions: you can't
deal with the banks directly, but you use a piece of hardware
(a card-reading terminal), which has been authorized by the
banks to integrators (eg, square), and transactions are
made through it. in the case of zelle, there is no hardware involved.