How to filter subcategory data from parent category in Laravel8 - ajax

Question

I want to filter subcategory data according to parent category.
I am getting all my subcategory inside all the categories. I tried many old answers from stackoverflow and youtube but not worked.
I want this filter inside my article post form.
create.article.blade.php
<form action="{{ URL::to('post-article-form') }}" method="post" enctype="multipart/form-data">
#csrf
<div class="form-group">
<label for="exampleInputEmail1">Article Name <b style="color: red">*</b></label>
<input type="text" class="form-control" id="exampleInputEmail1" aria-describedby="emailHelp" placeholder="Enter article title" name="articleTitle" required>
</div>
<div class="form-group">
<label for="exampleInputEmail1"> Select Article category </label>
<select class="form-control" name="category" id="category" required>
<option value=""> Select </option>
#foreach($categories as $category)
<option value="{{ $category->id }}"> {{ $category->name }}</option>
#endforeach
</select>
</div>
<div class="form-group">
<label for="exampleInputEmail1"> Select Sub category </label>
<select class="form-control" name="subCategory" id="subCategory" required>
<option value=""> Select </option>
#foreach($subCategories as $subCategory)
<option value="{{ $subCategory->id }}"> {{ $subCategory->name }}</option>
#endforeach
</select>
</div>
I used this below script for filter but not worked.
<script>
$('#category').on('change',function(e){
console.log(e);
var cat_id = e.target.value;
//ajax
$.get('/ajax-subcat?cat_id='+cat_id, function(data){
//subcategory
$('#subCategory').empty();
$('#subCategory').append($("<option></option>").val("").html("--Select Sub Category--"));
$.each(data,function(index, subcatObj){
$('#subCategory').append('<option value="'+subcatObj.id+'">'+subcatObj.name+'</option>');
})
})
});
</script>
My web.php route
//sub category
Route::get('add-sub-category', [SubCategoryController::class, 'create']);
Route::post('post-sub-category-form', [SubCategoryController::class, 'store']);
Route::get('subcategories', [SubCategoryController::class, 'index']);
Route::get("/ajax-subcat", function (Request $request){
$cat_id = $request-> Input::get('cat_id');
$subCategories = SubCategory::where('category_id',$cat_id)->get();
return response()->json($subCategories);
});