Advanced Shipping Price Rules - Shipping Cost on Category

The ‘Cost on Category’ advanced shipping rules works with your flat rate shipping rules and settings. 
Using this, you can apply shipping amount for a minimum and a maximum quantity of items belonging to the added category. And the amount or percentage entered in the ‘ Fee Amount’ field will be used for increasing, decreasing or using the same rate of shipping as per the category’s items in your cart.
How it works:
Let’s say you have mentioned minimum quantity as ‘x’ and maximum quantity as ‘x+12’. So, it has created a range of 12 items of a category.
 Now, to increase the amount for shipping for this range per added item count, keep the fee amount positive. To decrease the amount with increasing items, keep it negative.
 The fee amount will be added to the base flat rate shipping fee amount, which you’ve filled in the Fee section of the main form (Shipping Fee configuration) of this method. So, if you add $1, then the customers will be charged base fee + $1 for the x items while base fee + $5 for x+4 items.

Example 1:   Charge 12 to 24 items of Hoodie with Pocket Category with $10+

Advanced Shipping Price Rules - Shipping Cost on Category

Advanced Shipping Rules - Cost on Category

Example 2:  The Cost per category option is very similar to the shipping class. It has the same min/max condition and amount options.

Advane shipping cost per category

As shown in Cart Page:-

If product Category = Accessories is between 1 to 3, the Fee Amount is $3

Flat rate shipping method