Using Taefik with a non headless statefullset of pods

Traefik Traefik v3 (latest)
1

I have a statefulSet of pods running in my Kubernetes cluster.

apiVersion: apps/v1
kind: StatefulSet
metadata:
    name: webserver
    namespace: kube-system
    labes:
         app: webserver
    spec:
         replicas: 3
         selector:
             matchLabels:
                app: webserver
         template:
            metadata:
               labels:
                   app: webserver
            spec:
                containers:
                    name: php-apache-image
                    image: my.localregistry.local:5000/php_apache:0.0.1  # Or your           custom image
      ...
      ..

.

To use this "array of pods" I created the service

apiVersion: v1
kind: Service
metadata:
  name: service4webserver
  namespace: kube-system
spec:
  selector:
    app: webserver
  ports:
    - protocol: TCP
      port: 8080         # The port on which the Service listens for incoming traffic.
      targetPort: 80     # The port on the Pods to which the Service will forward the traffic.

This service will be directly called by another service which also will be called by a Traefik Ingress Controller. At the end, I need that any request arriving to service4webserver will be forwarded to the StatefulSet of pods and here be load balanced with Traefik. How to do this? Also, while at

it is said that to work with a StatefulSet services as service4webserver should be headless. However, I got service4webserver working well as a non headless service. Can this affect how to work with Traefik?

I am working with apiVersion: Traefik.io/alpha1 for my ingress route and the latest version of k3s version v1.33.3+k3s1 (236cbf25)
go version go1.24.4 and Traefik version 3.3.6

Thanks in Advance