Custom Authorizor question

What’s the api gateway request? Do you mean the method, such as PUT/POST/DELETE? or the paths that admin users can access specified?

This is the template for the methodArn you can define in policy when calls custom authorizer handler (Amazon API Gateway)

 "methodArn":"arn:aws:execute-api:<regionId>:<accountId>:<apiId>/<stage>/<method>/<resourcePath>"

So what you can define for different users are two parts only:

method - such as GET/PUT/POST/DELETE, etc
resourcePath -  define in apigateway path

And read this document as well to see if it is helpful for your question: