You're talking about variants but entries don't have variants, only products do.
And you can only assign custom item fields to categories of products, not entry fields.
To create custom item fields for a category of products, simply create one with the menu Display>Custom fields, select the table "item" and then the category you want it for in the categories listing area of the custom field. That's basically it. It will display automatically on the product page of all the products of that category.