Onclick of your refresh button, you could call the page event method ionViewWillEnter()

From the official docs --> ionViewWillEnter() Runs when the page is about to enter and become the active page.

HTML

<button (click)="refreshPage()">Refresh Page</button>

Typescript

    ionViewWillEnter(){
            this.myDefaultMethodToFetchData();
        }

    refreshPage() {
        this.ionViewWillEnter();
    }

    myDefaultMethodToFetchData(){
        ...Do Something, when the page opens...
    }

This will work!!! Give this under the function that's called on button click event.

this.navCtrl.setRoot(this.navCtrl.getActive().component);

or

Use the ionViewWillEnter lifecycle event on your page. You can put the correct code in that method to refresh all the necessary things on your page. https://ionicframework.com/docs/api/navigation/NavController/

Add this in the constructor and just replace your page name

    this.navigationSubscription = this.router.events.subscribe((e: any) => {
           if (e instanceof NavigationEnd && e.url === '/page-name' && localStorage.getItem('prevUrl') === '/page-name') {
            this.ionViewWillEnter();
            this.ngOnInit
           }
        });