Can I create data interaction between Server and Client with JWT, which use the same "secret"?

I try to create a Web application with JWT:

If a user send a request the server, I can run the process on the server and send the data back to the browser in a web token, that brings me to the question:

How can I verify this server response in the browser and send a new request to the server by using JWT with a secrete that can be accept from the server?

On the server the JWT from the browser request should be verify.

My consideration is to create a JWT on the client with the same "secret" but this is readable for attackers, because it is possible to read the source code (developer console).

Does there exist an way?

//Create request JWT
Request 1 --> {head: ...; data:..., secrete: secret}
//Request should be checkted on the server (secrete)  
// create a Resonse JWT and send back to the Client
Resonse 1 --> {head: ...; data:..., secrete: secret}
//Client verify the Respons JWT by the secrete