demo

class StudentController extends Controller
{
    public function index()
    {
        $students = Student::all();
        return view('students.index', compact('students'));
    }

public function store(Request $request)
    {
        $student = new Student();
        $student->student_name = $request->input('student_name');
        $student->mobile = $request->input('mobile');
        $student->save();
        return response()->json(['message' => 'Student added successfully']);
    }
}

<form id="studentForm">
        @csrf
        <input type="text" name="student_name" placeholder="Enter student name">
        <input type="text" name="mobile" placeholder="Enter student mobile">
        <button type="submit">Add Student</button>
    </form>
    <ul id="studentList">
        @foreach($students as $student)
            <li>{{ $student->student_name }} - {{ $student->student_name }}</li>
        @endforeach
    </ul>
    
    <script src="https://code.jquery.com/jquery-3.6.0.min.js"></script>
    <script>
        $(document).ready(function () {
            $('#studentForm').submit(function (e) {
                e.preventDefault();

$.ajax({
                    type: 'POST',
                    url: '/students',
                    data: $('#studentForm').serialize(),
                    success: function (response) {
                        $('#studentList').append('<li>' + $('input[name="student_name"]').val() +' - '+ $('input[name="mobile"]').val() + '</li>');
                        $('#studentForm')[0].reset();
                    }
                });
            });
        });
    </script>

Route::get('/', [StudentController::class, 'index']);
Route::post('/students', [StudentController::class, 'store']);