Generic type and dynamic type for the same property

Question

I have the following classes:

public interface IClass 
{
   // empty interface
}

Two classes implements the interface as a signature only

public abstract class TypeA : IClass
{
   ...
}

public abstract class TypeB : IClass
{
   ...
}

Then each of them has some concrete classes:

public class TypeA_1 : TypeA
{
   ...
}

public class TypeA_2 : TypeA
{
   ...
}

public class TypeB_1 : TypeB
{
   ...
}

public class TypeB_2 : TypeB
{
   ...
}

Then I want a model to have a list of object that under IClass, but that object will depend on the implementation of two methods.

When doing ReadMethod, I want the Model to have a list of TypeA (either TypeA_1 or TypeA_2) which is dynamically determined at run-time.

When doing WriteMethod, I want to Model to be a list of TypeB (either TypeB_1 or TypeB2) -- this can be done by using generic type e.g. public class Model<T> where T : IClass

public class Model
{
   IList<IClass> AListOfObject { get; set; }
}

Methods:

public Model ReadMethod(int a)
{
   List<IClass> list = null;

   // prepare Model with list of object (different kind based on argument "a")
   if (a == 1) 
   {
      list = new List<TypeA_1>{ ... };    ----- seems to be not working as instantiating different type?
   }
   if (a == 2) 
   {
      list = new List<TypeA_2>{ ... };
   }

   return new Model { AListOfObject = list };
}

public void WriteMethod(Model model)
{
   ...
}

Actually how can I define the Model that could fulfill this two methods at the same time? If I use generic type, it will fulfill the WriteMethod's need, but it won't work on the ReadMethod as it is dynamic.

Am I conceptually wrong to expect one single Model? Is it must to be 2 separate Model? But all of them are under IClass?

Also I'm just a bit confused on the reason why List<IClass> list = new List<TypeA_1>() won't work.