Check the official docs here for a similar use case. Create the secret using:
$ kubectl create secret generic my-secret --from-file=ssh-privatekey=/path/to/.ssh/id_rsa --from-file=ssh-publickey=/path/to/.ssh/id_rsa.pub
Now mount it using this pod config:
{
  "kind": "Pod",
  "apiVersion": "v1",
  "metadata": {
    "name": "secret-test-pod",
    "labels": {
      "name": "secret-test"
    }
  },
  "spec": {
    "volumes": [
      {
        "name": "secret-volume",
        "secret": {
          "secretName": "my-secret"
        }
      }
    ],
    "containers": [
      {
        "name": "ssh-test-container",
        "image": "mySshImage",
        "volumeMounts": [
          {
            "name": "secret-volume",
            "readOnly": true,
            "mountPath": "/etc/secret-volume"
          }
        ]
      }
    ]
  }
}
Kubernetes in itself does not have any way of controlling file permissions for a secret right now. You can check out this if it helps: