Interface with generic parameter vs Interface with generic methods

Your generic method implementation has to be generic as well, so it has to be:

public class MyConcrete2 : IMyInterface2
{
    public T My<T>()
    {
        throw new NotImplementedException();
    }
}

Why you can't do My<string>() here? Because interface contract needs a method, that could be called with any type parameter T and you have to fulfill that contract.

Why you can't stop genericness in this point? Because it would cause situations like following:

Class declarations:

public interface IMyInterface2
{
    T My<T>(T value);
}

public class MyClass21 : IMyInterface2
{
    public string My<string>(string value) { return value; }
}

public class MyClass22 : IMyInterface2
{
    public int My<int>(int value) { return value; }
}

Usage:

var item1 = new MyClass21();
var item2 = new MyClass22();

// they both implement IMyInterface2, so we can put them into list
var list = new List<IMyInterface2>();
list.Add(item1);
list.Add(item2);

// iterate the list and call My method
foreach(IMyInterface2 item in list)
{
    // item is IMyInterface2, so we have My<T>() method. Choose T to be int and call with value 2:
    item.My<int>(2);

    // how would it work with item1, which has My<string> implemented?
}

Because your interface declares a generic method T My<T>(), but you implementation does not implement a function with that specific signature.

To achieve what you want, you need to provide the T generic parameter to the interface instead, in your first example:

public interface IMyInterface2<T>
{
        T My();
}

public class MyConcrete2 : IMyInterface2<string>
{
    public string My()
    {
        throw new NotImplementedException();
    }
}