This article will be helpful for people who want to provide a discount based on the purchase of products with specific attributes.
Different scenarios:

The right way of using attributes in your products

Step 1: Pre-define the Attributes

VERY VERY IMPORTANT: When you create a variable product, always pre-define the Attributes in the Products -> Attributes section

Step 2:
Then, when you create the Variable product, choose these attributes, and add.

Now associate the attribute values and check the "Used for variations" checkbox.

IMPORTANT: Please DO NOT select the "custom product attribute".
If you use "Custom Product Attributes" that is created on-the-fly, then the attribute specific discount will NOT apply. Because WooCommerce does not create any attributes when you use a custom product attribute.

Let us create an example rule :
Navigate to Woocommerce -> Woo Discount Rules -> Add New Rule.

After Entering into the rule page, just add the rule name and you can select the desired discount adjustment type from the Drop-down.

Scenario 1 :
Discount on M-sized Tshirts.

Product Adjustment is chosen and since our discount scenario applies to an attribute, you can choose Attributes in the filter.

Here is a screenshot of rule setup:

Screenshot of cart page:

Scenario 2:

Provide a free product on purchase "M" size T-shirts.

Buy X get Y is chosen and the discount product is entered in the Get Discount.

Here is a screenshot of rule setup:

Screenshot of cart page:

Advanced Scenario

Buy one get one Free/discount with the attributes.

Apply Discount within the L sized T-shirts.

You can choose to apply within the cheapest/highest priced.

In order to achieve your requirement, we must first load the attribute in the category dropdown in our plugin.

You can load Attributes in Category listing via a code snippet. Then you can choose the attribute to which the Buy X Get Y cheapest applies to.

Please follow these steps below:
Step 1:

Load Attribute in the Category list
To load the attributes like categories, you can use this snippet --> https://gist.github.com/AnanthFlycart/5c1d29ea318550bc35a90747db9f6d30

Note: For attributes, the taxonomy will start with prefix pa_ in the above snippet. You can replace the attribute which you would like to load for example "pa_size" in the 4th line.

You can install this snippet via code snippet plugin.
Here is a guide which might be of help :
https://docs.flycart.org/en/articles/2404915-using-code-snippets-plugin

Step 2 :

Then you can set up the Buy X get Y type of discount for specific categories and select the attribute you want to give for discounts.

Here is a screenshot of rule setup:

Now, the discount will be applied to attribute "medium" in the cart.

Note :
The same approach can be adopted for other Buy One get One based Attribute Discount Rules as well.

Video:

I have more questions
Please submit a support request. We are always happy to assist you :)