Not the way you have written it. What you want to do is a little backwards in your thinking.
Public methods in your base class will be available to all classes which inherit from it.
If you need a method to be available only to a specific child, then you must define that method only in that class and not the base.
Note that your naming convention is a little strange. See my example for what I think you are aiming at.
For example:
public class Base
{
public void Method1(){ Console.WriteLine("Method 1 called."); }
abstract void Method2();
}
public class Hide : Base
{
public override void Method2(){ Console.WriteLine("Method 2 called in Hide."); }
public void Method3(){ Console.WriteLine("Method 3 called."); }
}
public class Child : Base
{
public override void Method2(){ Console.WriteLine("Method 2 called in Child."); }
public void Method4(){ Console.WriteLine("Method 3 called."); }
}