Try to create two Ingresses first by default without any restriction:
apiVersion: extensions/v1beta1
 kind: Ingress
 metadata:
 name: ingress-test
 spec:
   rules:
   - host: host.host.com
   http:
      paths:
        - path: /service-mapping
      backend:
         serviceName: /service-mapping
         servicePort: 9042
Then, create a secret for auth as described in the doc:
Creating the htpasswd
$ htpasswd -c auth foo
New password: <bar>
New password:
Re-type new password:
Adding password for user foo
Creating the secret:
$ kubectl create secret generic basic-auth --from-file=auth
secret "basic-auth" created
Second Ingress with auth for paths which you need to restrict:
apiVersion: extensions/v1beta1
kind: Ingress
metadata:
  name: ingress-with-auth
  annotations:
    # type of authentication
    nginx.ingress.kubernetes.io/auth-type: basic
    # name of the secret that contains the user/password definitions
    nginx.ingress.kubernetes.io/auth-secret: basic-auth
    # message to display with an appropiate context why the authentication is required
    nginx.ingress.kubernetes.io/auth-realm: "Authentication Required - foo"
spec:
  rules:
  - host: host.host.com
    http:
      paths:
      - path: /admin
        backend:
          serviceName: service_name
          servicePort: 80