To redirect the user to a specific Activity based on your logic you can use PendingIntent.
To check a working example click here.
OR
try below code on button click.
NotificationCompat.Builder builder = new NotificationCompat.Builder(this);
builder.setSmallIcon(android.R.drawable.ic_dialog_alert);
Intent intent = new Intent(Intent.ACTION_VIEW, Uri.parse("https://www.stackoverflow.com/"));
PendingIntent pendingIntent = PendingIntent.getActivity(this, 0, intent, 0);
builder.setContentIntent(pendingIntent);
builder.setLargeIcon(BitmapFactory.decodeResource(getResources(), R.mipmap.ic_launcher));
builder.setContentTitle("Notifications Title");
builder.setContentText("Your notification content here.");
builder.setSubText("Tap to view the website.");
NotificationManager notificationManager = (NotificationManager) getSystemService(NOTIFICATION_SERVICE);
// Will display the notification in the notification bar
notificationManager.notify(1, builder.build());
To check if your app is in the foreground or not Check out this post.