I have a base class test define below
type
Tinfo = procedure of object;
Test = class(TObject)
public
  procedure Add    ( const a : Tinfo ); reintroduce ;
end;
procedure Test.Add(const a: Tinfo);
begin
  Writeln('base class add function');
  // dosomething more  
end;
and I have a derived generic class from this base class
TTesting<T> = class(Test)
   public
     procedure Add    ( const a : T  ); reintroduce ;
   end;
and I am typecasting T to Tinfo but it gives me the error 
procedure TTesting<T>.Add(const a : T );
begin
  inherited Add(Tinfo(a) );  // gives me error here 
end;
is there any way I can implement this?
                        
First your cast is wrong, you obviously want to cast a and not T.
However if you want to type cast on a procedure of object which is a type that cannot be polymorphic in any way it makes no sense to put that into a generic type at all.
What should T be? It only can be a TInfo in your code.
If you however want T to be any event/method type you should store a TMethod in your base class and then work with that in your generic class. But remember that you cannot have a constraint that limits T to be an event type. So you might check that in your constructor.