how to prevent flutter showBottomSheet from being dismissed by dragging down?

Just wrap your child with GestureDetector and set onVerticalDragStart: (_) {},

showBottomSheet(
  context: context,
  builder: (context) => GestureDetector(
    child: *your_widget*,
    onVerticalDragStart: (_) {},
  ),
 
);

If you use showModalBottomSheet, simply use enableDrag property:

showModalBottomSheet(
  context: context,
  builder: (context) => yourWidget,
  enableDrag: false,
);

Set enableDrag property of BottomSheet to false its true by default

BottomSheet(
  enableDrag: false,
  builder: //builder
),

Refer here for more info on BottomSheet

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