Relationship between category and product

I have a nested category, n-level deep. Some categories have children and others don't. I want to be able to add products to a category such that when i query the product model i should be able to access the products related to that specific category.

I want to be able to use the result as json and access the products in the result.

My challenge here is that when i call the relation ship, the product is attached to the top level category even though it belongs to a category n-level deep.

Here's my Category and Product Model

<?php

namespace App\Models;

use Illuminate\Database\Eloquent\Factories\HasFactory;
use Illuminate\Database\Eloquent\Model;

class Category extends Model
{
    use HasFactory;

    /**
     * The attributes that are mass assignable.
     *
     * @var string[]
     */
    protected $fillable = [
        'title',
        'subtitle',
        'category_id',
        'img',
        'video',
        'status',
    ];

    public function parent()
    {
        return $this->belongsTo(Category::class, 'category_id');
    }

    public function children()
    {
        return $this->hasMany(Category::class, 'category_id');
    }

    public function product() {
        return $this->hasMany(Product::class);
    }
}

Product Model

<?php

namespace App\Models;

use Illuminate\Database\Eloquent\Factories\HasFactory;
use Illuminate\Database\Eloquent\Model;

class Product extends Model
{
    use HasFactory;

    protected $fillable = [
        'image',
        'video',
        'title',
        'discount',
        'time_taken',
        'max_quantity',
        'price',
        'status',
        'which_to_show',
        'category_id',
        'sub_category_id',
        'child_category_id',
        'product_description'
    ];

    public function category() {
        return $this->belongsTo(Category::class, 'category_id');
    }

    public function ratings()
    {
        return $this->hasMany(Rating::class);
    }
}

Product Controller

<?php
namespace App\Http\Controllers\Api\General;

use App\Http\Controllers\Controller;
use App\Models\PartnerService;

class ProductAPIController extends Controller {

    public function category_services () {
        $product = Product::select([
            'id',
            'image',
            'video',
            'title',
            'discount',
            'time_taken',
            'max_quantity',
            'price',
            'status',
            'which_to_show',
            'category_id',
            'sub_category_id',
            'child_category_id',
            'service_description'
        ])->with('category')
        ->orderBy('title', 'asc')
        ->get();

        $response = [
            'product'    =>  $product
        ];

        return response()->json($response, 200);
    }
}