How can I create a Drawer below status bar in Flutter?

For this kind of scenario, Flutter has the SafeArea widget. This widget will make sure that nothing is rendered e.g. beneath the status bar, i.e. a padding is added.

To apply this to your Drawer, you can simply wrap your Drawer with a SafeArea:

Scaffold(
  drawer: SafeArea(
    child: Drawer(..),
  ),
  ..
)

Screenshot of the drawer

You can also specify if you want to remove some of the padding added by SafeArea using the optional parameters top, bottom, left & right, e.g. SafeArea(bottom: false, ..).

Adding the padding: const EdgeInsets.all(0.0), to ListView resolves the issue.