procedure TForm1.Button1Click(Sender: TObject);
begin
  if not Assigned(FTableButton) then begin
    FTableButton := TButton.Create(self);
    FTableButton.Parent := self;
    FTableButton.Caption := 'I am New';
    FTableButton.OnMouseDown := TableButtonMouseDown;
    FTableButton.OnMouseMove := TableButtonMouseMove;
    FTableButton.OnMouseUp := TableButtonMouseUp;
  end;
end;

procedure TForm1.TableButtonMouseDown(Sender: TObject; Button: TMouseButton;
  Shift: TShiftState; X, Y: Integer);
begin
  FTableButtonDragging := true;
  FMouseDownLocation := Mouse.CursorPos;
  FButtonStartingLocation := TPoint.Create(FTableButton.Left, FTableButton.Top);
end;

procedure TForm1.TableButtonMouseMove(Sender: TObject; Shift: TShiftState; X,
  Y: Integer);
begin
  if FTableButtonDragging then begin
    FTableButton.Left := FButtonStartingLocation.X + (Mouse.CursorPos.X - FMouseDownLocation.X);
    FTableButton.Top := FButtonStartingLocation.Y + (Mouse.CursorPos.Y - FMouseDownLocation.Y);
    FTableButton.Invalidate;
  end;
end;

procedure TForm1.TableButtonMouseUp(Sender: TObject; Button: TMouseButton;
  Shift: TShiftState; X, Y: Integer);
begin
  FTableButtonDragging := false;
end;