Help with querying product filter

I want to sort listed products in the category selected, i need help with the controller querying.

My Blade File

@extends('layouts.cat5')

@section('content')
@include('frontEnd.ourJs')

    <div class="contact-container" style="align-items: flex-start;">
        <div class="form-container lcontact-form" style="width: 100%;">
            <h3 style="margin-bottom: revert; margin-top:12px;">Filter Category</h3>
                <div style="display: inline-block; margin-top:12px; text-align: center;">
                    <input type="text" id="catID" value="{{$catByUser}}" hidden/>
                    <input type="number" id="minpriceID" min="0" class="form-control" style="margin: inherit;" placeholder="Min Price">
                    <input type="number" id="maxpriceID" min="0" class="form-control" style="margin: inherit;" placeholder="Max Price">
                    <input type="text" id="search" class="form-control" style="margin: inherit;" placeholder="search product by name">
                    <div style="margin-top:inherit;">
                        <button class="login-btn form-control" id="findBtn" style="margin: inherit; border-left: inset;"> <span class="fas fa-filter"></span> Filter</button>
                    </div>
                </div>
        </div>
        <div class="gender-clothing">
            <div class="title-row">
                <div class="main-title">
                <h3 style="font-size: xx-large;">{{$catname->name}} Category</h3>
                </div>
            </div>
            <div class="cloth-row">
            @if(count($data)=="0")
                <h1 align="center" style="margin-top:20px">
                    No products found under
                <b style="color:red">{{$catByUser}} </b>
                    Category
                </h1>
            @elseif (count($data)!="0")
                    @foreach($data as $p)
                        <div class="cloth" id="productData">
                            <div class="card">
                            <img src="/products/large/{{$p->image}}" alt="{{$p->image}}" style="width:100%">
                            <h1 style="margin-top: revert;">{{$p->p_name}}</h1>
                            <br>
                            <p class="price" style="color:#0d6cb3;">NGN {{$p->price}}</p>
                            <br>
                            <p><a href="/product-detail/{{$p->id}}/{{$p->slug}}"><button>Explore</button></a></p>
                            </div>
                        </div>
                    @endforeach
            @endif
            </div>
        </div>
    </div>
        


<!-- <div class="container">
        <div class="row">
            <div class="col-sm-3">
                
            </div>
            <div class="col-sm-9 padding-right">
                @if(count($data)!="0")
                    <h1 class="text-center">{{$catByUser}} </h1>
                        <div class="row">
                                <div class="">

                                    <select id="catID">
                                        <option value="{{$catByUser}}">{{$catname->name}}</option>
                                    </select>

                                </div>
                                <div class="">
                                    <select id="priceID">
                                        <option value="">Select Price Range</option>
                                        <option value="100">0-100</option>
                                        <option value="100-300">100-300</option>
                                        <option value="300-500">300-500</option>
                                        <option value="500-1000">500-1000</option>
                                    </select>
                                    <input type="number" id="priceID">
                                </div>


                            <div class="col-sm-6 hidden-xs">
                                <div class="row">

                                    <div class="col-sm-4 pull-right">
                                        <button id="findBtn" class="btn btn-success">Find</button>
                                    </div>
                                    <div class="styleNm">16 style(s)</div>
                                </div>
                            </div>
                    @endif
                        </div>
                        <div class="row top25">


                    @if(count($data)=="0")
                    <div class="col-md-12" align="center">

                        <h1 align="center" style="margin:20px">
                        No products found under
                        <b style="color:red">{{$catByUser}} </b>
                            Category </h1>

                    </div>
                    @else
                    <div id="productData">
                    @foreach($data as $p)
                    <div class="col-xs-6 col-sm-4" >
                                <div class="itemBox">
                                    <div class="prod">
                            <img
                            src="/products/large/{{$p->image}}" alt="/products/large/{{$p->image}}"
                            width="400px" height="360px" /></div>
                                    <label>{{$p->p_name}}</label>
                                    <span class="hidden-xs">Code: {{$p->p_code}}
                        <br>
                        {{$p->pro_info}}</span>
                                    <div class="addcart">
                                        <div class="price">NGN {{$p->price}}</div>
                                        <div class="cartIco hidden-xs"><a href="{{url('/cart/add')}}/{{$p->id}}"></a></div>
                                    </div>
                                </div>
                            </div>
                    @endforeach
                    </div>
                @endif
            </div>
        </div>
    </div> -->

@endsection

ourJs

<script>
$(document).ready(function(){
  $("#findBtn").click(function(){
    var cat = $("#catID").val();
    var minprice = $('#minpriceID').val();
    var maxprice = $('#maxpriceID').val();
    var search = $('#search').val();
    
    $.ajax({
      type: 'get',
      dataType: 'html',
      url: '{{url('/productsCat')}}',
      data: 'cat_id=' + cat + 'min_price=' + minprice + 'max_price' + maxprice + 'search' + search,
      success:function(response){
        console.log(response);
        $("#productData").html(response);
      }
    });
  });
});
</script>

Web Route

Route::get('/selected-category/{id}/{slug}', 'SelectedCategoryController@show')->middleware('auth');
Route::get('selected-category/{id}/{slug}','SelectedCategoryController@show');
Route::get('productsCat','SelectedCategoryController@productsCat');

Controller

public function show($id, $slug, Request $request)
    {
        $cat = $id;
        // dd($cat);
        $catByUser = $cat;
        $catname = ProductCategory::find($slug);
        $subcategory = SubCategory::with(['productCategory'])->orderBy('name')->get();
        $data = Product::where('categories_id', $cat)->get();
        // dd($catname);
        $cart = User::findorfail(auth()->user()->id)->cart;
        $user = auth()->user()->id;
        $messages = User::findorfail($user)->latestmessaging->count();
        // dd($category);
        return view('frontEnd.product-category', compact('data', 'catname', 'catByUser', 'subcategory', 'cart', 'messages'));
    }

    public function productsCat(Request $request){
        
        $cat_id = $request->cat_id;
        // dd(count($request->price));
        $pricemax= $request->max_price;
        $pricemin= $request->min_price;
	$search= $request->search;
 
     }

I need help with the querying...