Flutter - Open Modal Bottom Sheet on Bottom navigation bar item click

try this:

class _MyNavigationBarState extends State<MyNavigationBar > {
  int _currentTabIndex = 0;

  @override
  Widget build(BuildContext context) {
    final _kTabPages = <Widget>[
      Page1(),
      Page2(),
      Page3(),
      Container(),
    ];
    final _kBottmonNavBarItems = <BottomNavigationBarItem>[
      const BottomNavigationBarItem(icon: Icon(Icons.home), label: 'Home'),
      const BottomNavigationBarItem(icon: Icon(Icons.network_cell), label: 'Prices'),
      const BottomNavigationBarItem(icon: Icon(Icons.add_circle), label: 'Trade'),
      const BottomNavigationBarItem(icon: Icon(Icons.account_balance_wallet), label: 'Wallet'),
    ];
    assert(_kTabPages.length == _kBottmonNavBarItems.length);
    final bottomNavBar = BottomNavigationBar(
      items: _kBottmonNavBarItems,
      currentIndex: _currentTabIndex,
      type: BottomNavigationBarType.fixed,
      onTap: (int index) {
        if(index == 3){
          showBottomSheet();
          return;
        }

        setState(() {
          _currentTabIndex = index;
        });
      },
    );
    return Scaffold(
      body: _kTabPages[_currentTabIndex],
      bottomNavigationBar: bottomNavBar,
      ),
    );
  }
}

showBottomSheet(){
      Container _buildBottomSheet(BuildContext context) {
    return Container(
      height: 300,
      padding: const EdgeInsets.all(8.0),
      decoration: BoxDecoration(
        border: Border.all(color: Colors.blue, width: 2.0),
        borderRadius: BorderRadius.circular(8.0),
      ),
      child: ListView(
        children: <Widget>[
          const ListTile(title: Text('Bottom sheet')),
          const TextField(
            keyboardType: TextInputType.number,
            decoration: InputDecoration(
              border: OutlineInputBorder(),
              icon: Icon(Icons.attach_money),
              labelText: 'Enter an integer',
            ),
          ),
          Container(
            alignment: Alignment.center,
            child: ElevatedButton.icon(
              icon: const Icon(Icons.save),
              label: const Text('Save and close'),
              onPressed: () => Navigator.pop(context),
            ),
          )
        ],
      ),
    );
  }
}

implement like this

import 'package:flutter/material.dart';

void main() {
  runApp(const MyApp());
}

class MyApp extends StatelessWidget {
  const MyApp({Key? key}) : super(key: key);

  @override
  Widget build(BuildContext context) {
    return MaterialApp(
      title: 'Flutter Demo',
      theme: ThemeData(
        primarySwatch: Colors.blue,
      ),
      home: const MyHomePage(title: 'Flutter Demo Home Page'),
    );
  }
}

class MyHomePage extends StatefulWidget {
  const MyHomePage({Key? key, required this.title}) : super(key: key);
  final String title;

  @override
  State<MyHomePage> createState() => _MyHomePageState();
}

class _MyHomePageState extends State<MyHomePage> {
  int _selectedIndex = 0;
  static const TextStyle optionStyle = TextStyle(fontSize: 30, fontWeight: FontWeight.bold);
  static const List<Widget> _widgetOptions = <Widget>[
    Text(
      'Index 0: Home',
      style: optionStyle,
    ),
    Text(
      'Index 1: Business',
      style: optionStyle,
    ),
    Text(
      'Index 2: School',
      style: optionStyle,
    ),
    Text(
      'Index 3: Settings',
      style: optionStyle,
    ),
  ];

  void _onItemTapped(int index) {
    setState(() {
      _selectedIndex = index;
    });

    showModalBottomSheet<void>(
      context: context,
      builder: (BuildContext context) {
        return Container(
          height: 200,
          color: Colors.amber,
          child: Center(
            child: Column(
              mainAxisAlignment: MainAxisAlignment.center,
              mainAxisSize: MainAxisSize.min,
              children: <Widget>[
                Text('BottomSheet $index'),
                ElevatedButton(
                  child: Text('Close BottomSheet $index'),
                  onPressed: () => Navigator.pop(context),
                )
              ],
            ),
          ),
        );
      },
    );
  }

  @override
  Widget build(BuildContext context) {
    return Scaffold(
      appBar: AppBar(
        title: const Text('BottomNavigationBar Sample'),
      ),
      body: Center(
        child: _widgetOptions.elementAt(_selectedIndex),
      ),
      bottomNavigationBar: BottomNavigationBar(
        items: const <BottomNavigationBarItem>[
          BottomNavigationBarItem(
            icon: Icon(Icons.home),
            label: 'Home',
            backgroundColor: Colors.red,
          ),
          BottomNavigationBarItem(
            icon: Icon(Icons.business),
            label: 'Business',
            backgroundColor: Colors.green,
          ),
          BottomNavigationBarItem(
            icon: Icon(Icons.school),
            label: 'School',
            backgroundColor: Colors.purple,
          ),
          BottomNavigationBarItem(
            icon: Icon(Icons.settings),
            label: 'Settings',
            backgroundColor: Colors.pink,
          ),
        ],
        currentIndex: _selectedIndex,
        selectedItemColor: Colors.amber[800],
        onTap: _onItemTapped,
      ),
    );
  }
}