how to access the same data from different classes without a reference or something?

If you make the "right and only" data-storing base class a singleton, or static class, then yes. Unfortunately, then you can't usefully derive from it and have multiple instances of the derived classes.

To be honest, what you are trying to do sounds like bad design, and will probably give you more problems in the long run than you will solve in the short term.

What are you actually trying to do, that you think you need this?

If you have

public class BaseClass
{
   public string BaseClassProperty{get;set;}
}

then you have

public class FirstClass : BaseClass
{

}

and in some code you have

FirstClass instantiation = new FirstClass();

Then you can say

instantiation.BaseClassproperty = 42;

i.e. you access the data stored in the base class

If, however, you want to also do this

FirstClass instantiation = new FirstClass();
FirstClass otherinstantiation = new FirstClass();
instantiation.BaseClassProperty = 42;

and then want to do

int i = otherinstantiation.BaseClassproperty;

and want i to = 42, then you need to make the property Static

e.g.

public class BaseClass
{
   public static string BaseClassProperty{get;set;}
}

and then from anywhere in your code you can access the property..

int i = BaseClass.BaseClassProperty;

(this is pretty much what Paulo said above, but more verbose!)