C# - How do you GetComponent of a child class that inherits from a specific class?

I think this answers what you mean. The short and painless answer to getting a specific child script by its' type dynamically without actually searching for its' type is... you can't. However, you don't need to do this.

Virtual and Abstract:

Virtual and Abstract can be used to make a method in the base script behave differently in a child script. The great thing about this is that say for example we have a script, "Sword," that is a child of "Item." We can get the sword as type "item" and call its' function "sword.Equip()" that we defined in the "Sword" script. See here for a little more detail

Time for some pseudo-code, as this concept took some time for me to understand:

 public class Item
 {
     public virtual void Equip()
     {
         Debug.Log("Equipped an item.");
     }
 }
 
 public class Sword: Item
 {
     public string swordName = "Sword of Death";
     public override void Equip()
     {
         base.Equip(); // This is not necessary, but it calls the Item.Equip() function as-is, in case you need it
         Debug.Log("Equipped item name is " + swordName");
     }
 }
 
 void EquipHoveredItem(GameObject hoveredItem)
 {
     Item item = hoveredItem.GetComponent<Item>();
     if (item != null)
     {
         item.Equip(); // Debugs "Equipped an item." "Equipped item name is Sword of Death"
     }      
 }

Now, if you wanted to get specific properties from one of your children script, then I would just put the property on your parent script. That way each item will have the property, but whether or not it is used depends on the item.