change the endpoint to point to your API. /api/myservice/my-api or use app-root annotation, to point to your api inside /api/myservice:

nginx.ingress.kubernetes.io/app-root: /path/to/my/app/root/dir

more details here: https://kubernetes.github.io/ingress-nginx/user-guide/nginx-configuration/annotations/#rewrite

Best way to achieve this would be to remove the prometheus endpoint from ingress and if you are aware prometheus supports auto discovery using annotations on the service, configure prometheus for k8s auto discovery and then add annotations in you service yaml file. https://prometheus.io/docs/prometheus/latest/configuration/configuration/#kubernetes_sd_config

You can add an Ingress rule that redirects the endpoint to the default-backend:

apiVersion: extensions/v1beta1
kind: Ingress
metadata:
  name: block
  annotations:
    ingress.kubernetes.io/ssl-redirect: "true"
    ingress.kubernetes.io/rewrite-target: /
spec:
  tls:
  - hosts:
    - myapp.to
  rules:
  - host: myapp.to
    http:
      paths:
      - path: /metrics
        backend:
          serviceName: ingress-default-backend
          servicePort: 8080

If you just need internal access, I don't think you should put it into ingress. You could make use of the DNS Service together with Kubernetes cluster already.

If your prometheus service is running the same namespace as your working pod, you could use following address to access it.

http://prometheus-svc-name

If your prometheus service is running in a different namespace, you could use:

http://prometheus-svc-name.prometheus-namespace.svc.cluster.local

to access the service.

Update:

More clear about the question after comments.

You could write another rule to hide your /prometheus endpoint like this:

ingress:
  enabled: true
  annotations:
    kubernetes.io/ingress.class: nginx
    // ...
  paths:
    - /api/myservice => myservice
    - /api/myservice/prometheus => 404 default backend.

nginx-ingress will match the longest route first. It will route /api/myservice/prometheus to 404. See this documentation