Additionally to what @Tarun Khosla mentioned which is correct, there is another stackoverflow question with examples which might be helpful. I am posting this as a community wiki answer for better visibility for the community, feel free to expand on it.

There are 2 examples provided by @Nick Rak

I’ve faced the same issue and found the solution on github. To achieve your goal, you need 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

According to sedooe answer, his solution may have some issues.

and @sedooe

You can use server-snippet annotation. This seems like exactly what you want to achieve.

Make a custom backend using below

apiVersion: apps/v1
kind: Deployment
metadata:
  name: custom-http-backend
spec:
  selector:
    matchLabels:
      app: custom-http-backend
  template:
    metadata:
      labels:
        app: custom-http-backend
    spec:
      containers:
      - name: custom-http-backend
        image: inanimate/echo-server
        ports:
        - name: http
          containerPort: 8080
        imagePullPolicy: IfNotPresent
---
apiVersion: v1
kind: Service
metadata:
  name: custom-http-backend
spec:
  selector:
    app: custom-http-backend
  ports:
    - protocol: TCP
      port: 80
      targetPort: 8080

Then in your ingress add this rule

- host: ingress.example.com
    http:
      paths:
      - path: /
        backend:
          serviceName: custom-http-backend
          servicePort: 80