I have a templated class A
You can't with your current approach. one_type is an alias to a particular template specialization, so it gets whatever code the template has.
If you want to add code specific to one_type, you have to declare it as a subclass of A specialization, like this:
class one_type:
public A
{
one_type(int m)
: A(m)
{
cerr << "One type" << endl;
}
};