Unable to fetch metrics from custom metrics API: the server is currently unable to handle the request

First of all, confirm that the Metrics Server POD is running in your kube-system namespace. Also, you can use the following manifest:

---
apiVersion: v1
kind: ServiceAccount
metadata:
  name: metrics-server
  namespace: kube-system
---
apiVersion: extensions/v1beta1
kind: Deployment
metadata:
  name: metrics-server
  namespace: kube-system
  labels:
    k8s-app: metrics-server
spec:
  selector:
    matchLabels:
      k8s-app: metrics-server
  template:
    metadata:
      name: metrics-server
      labels:
        k8s-app: metrics-server
    spec:
      serviceAccountName: metrics-server
      volumes:
      # mount in tmp so we can safely use from-scratch images and/or read-only containers
      - name: tmp-dir
        emptyDir: {}
      containers:
      - name: metrics-server
        image: k8s.gcr.io/metrics-server-amd64:v0.3.1
        command:
        - /metrics-server
        - --kubelet-insecure-tls
        - --kubelet-preferred-address-types=InternalIP
        imagePullPolicy: Always
        volumeMounts:
        - name: tmp-dir
          mountPath: /tmp

If so, take a look into the logs and look for any stackdriver adapter’s line. This issue is commonly caused due to a problem with the custom-metrics-stackdriver-adapter. It usually crashes in the metrics-server namespace. To solve that, use the resource from this URL, and for the deployment, use this image:

gcr.io/google-containers/custom-metrics-stackdriver-adapter:v0.10.1

Another common root cause of this is an OOM issue. In this case, adding more memory solves the problem. To assign more memory, you can specify the new memory amount in the configuration file, as the following example shows:

apiVersion: v1
kind: Pod
metadata:
  name: memory-demo
  namespace: mem-example
spec:
  containers:
  - name: memory-demo-ctr
    image: polinux/stress
    resources:
      limits:
        memory: "200Mi"
      requests:
        memory: "100Mi"
    command: ["stress"]
    args: ["--vm", "1", "--vm-bytes", "150M", "--vm-hang", "1"]

In the above example, the Container has a memory request of 100 MiB and a memory limit of 200 MiB. In the manifest, the "--vm-bytes", "150M" argument tells the Container to attempt to allocate 150 MiB of memory. You can visit this Kubernetes Official Documentation to have more references about the Memory settings.

You can use the following threads for more reference GKE - HPA using custom metrics - unable to fetch metrics, Stackdriver-metadata-agent-cluster-level gets OOMKilled, and Custom-metrics-stackdriver-adapter pod keeps crashing.

What do you get for kubectl get pod -l "app.kubernetes.io/instance=api,app.kubernetes.io/name=api-name"? There should be a pod, to which the service reffers. If there is a pod, check its logs with kubectl logs <pod-name>. you can add -f to kubectl logs command, to follow the logs.