Icon Badge Count

action_bar_notifications.xml

<?xml version="1.0" encoding="utf-8"?>
<menu xmlns:android="http://schemas.android.com/apk/res/android"
        xmlns:app="http://schemas.android.com/apk/res-auto">
    <item
            android:id="@+id/notifications"
            android:orderInCategory="100"
            android:title=""
            android:icon="<-- your drawable icon here-->" 
            app:actionLayout="@layout/notification_icon_badge"
            app:showAsAction="always" />
</menu>

badge_background.xml

<?xml version="1.0" encoding="utf-8"?>
<shape xmlns:android="http://schemas.android.com/apk/res/android" android:shape="oval">

    <solid android:color="@android:color/holo_red_dark"/>
    <stroke android:color="@android:color/white" android:width="1dp"/>

</shape>

BadgeCount.kt

// Create action bar item (notification icon)
    override fun onCreateOptionsMenu(menu: Menu): Boolean {

        // Inflate the menu; this adds items to the action bar if it is present.
        menuInflater.inflate(R.menu.action_bar_notifications, menu)

        // Get the menu item
        var menuItem = menu.findItem(R.id.notifications)
        
        // Get the view of the menu item
        val actionView = menuItem.actionView
        
        // Get the badge inside the action view
        var badgeCount = actionView.findViewById(R.id.cart_badge) as TextView
        
        // Manipulate the badge
        badgeCount.visibility = View.VISIBLE
        badgeCount.text = "12"

        // Set on click action
        actionView.setOnClickListener {
            val intent = Intent(this, HomeNotificationsActivity::class.java)
            startActivity(intent)
        }
        return true
    }

notification_icon_badge.xml

<?xml version="1.0" encoding="utf-8"?>
<FrameLayout
        style="?attr/actionButtonStyle"
        xmlns:android="http://schemas.android.com/apk/res/android"
        android:layout_width="wrap_content"
        android:layout_height="wrap_content"
        android:clipToPadding="false"
        android:focusable="true">

    <ImageView
            android:layout_width="wrap_content"
            android:layout_height="wrap_content"
            android:layout_gravity="center"
            android:src="<-- your drawable icon here-->"/>

    <TextView
            android:id="@+id/cart_badge"
            android:layout_width="20dp"
            android:layout_height="20dp"
            android:layout_gravity="right|end|top"
            android:layout_marginEnd="-5dp"
            android:layout_marginRight="-5dp"
            android:layout_marginTop="3dp"
            android:background="@drawable/badge_background"
            android:gravity="center"
            android:padding="3dp"
            android:textColor="@android:color/white"
            android:text="0"
            android:textSize="10sp"/>

</FrameLayout>

source: https://stackoverflow.com/questions/43194243/notification-badge-on-action-item-android