create a separate StatefulWidget for the showModalBottomSheet(), like
 showModalBottomSheet(
    context: context,
    builder: (ctx) {
      return MapBottomSheet();
    });
Bottom Sheet Statefulwidget
class MapBottomSheet extends StatefulWidget {
  @override
  _MapBottomSheetState createState() => _MapBottomSheetState();
}
class _MapBottomSheetState extends State<MapBottomSheet> {
  List<String> places = [];
  void _setPlaces(String place) {
    setState(() {
      places.add(place);
    });
  }
  @override
  Widget build(BuildContext context) {
    return Container(
      color: Colors.black12,
      child: Column(
        children: [
          AppTextField(
            hint: "Search",
            onEditingComplete: () {},
            onChanged: (String text) {},
            onSubmitted: (String text) async {
              // Await the http get response, then decode the json-formatted response.
              var response = await http.get(Uri.parse(
                  'https://api.mapbox.com/geocoding/v5/mapbox.places/$text.json?access_token=pk.eyJ1IjoidjNyc2lvbjkiLCJhIjoiY2ttNnZldmk1MHM2ODJxanh1ZHZqa2I3ZCJ9.e8pZsg87rHx9FSM0pDDtlA&country=PK&fuzzyMatch=false&place=park'));
              if (response.statusCode == 200) {
                Map<String, dynamic> data = jsonDecode(response.body);
                print(data.toString());
                List<dynamic> features = data['features'];
                features.forEach((dynamic feature) {
                  setState(() {
                    _setPlaces(feature['place_name']);
                  });
                });
              } else {
                print('Request failed with status: ${response.statusCode}.');
              }
            },
          ),
          Expanded(
            child: Container(
              height: 250.0,
              width: double.infinity,
              child: ListView.builder(
                  itemCount: places.length,
                  itemBuilder: (ctx, idx) {
                    return Container(
                      child: Text(places[idx]),
                    );
                  }),
            ),
          ),
        ],
      ),
    );
    
  }
}