Multi Parameter in Search 'GET'

Append the parameters to pagination links:

From docs:

Appending To Pagination Links

You may append to the query string of pagination links using the appends method. For example, to append sort=votes to each pagination link, you should make the following call to appends:

{{ $users->appends(['sort' => 'votes'])->links() }}

If you wish to append all current query string values to the pagination links you may use the withQueryString method:

{{ $users->withQueryString()->links() }}

Also try moving your paginate to just before return view:

$product->paginate(10);

Example:

       $query = Dog::where('dogname', 'like', $dogsch);
        if ($aval == "n") {
            $query->where('adopted', '=', 1);
        } else if ($aval == "y") {
            $query->where('adopted', '=', 0);
        }
        $dogs = $query->orderBy('lastedit', 'DESC')->paginate(5);

       $params = array('psch' => $dogsearch, 'aval' => $aval);

And view:

{{ $dogs->appends($params)->links() }} 

my problem not in pagination, my problem how to get data from the database depend on the query parameter, the query parameter may be sent or may be null.

Just like I did here:

        if ($aval == "n") {
            $query->where('adopted', '=', 1);
        } else if ($aval == "y") {
            $query->where('adopted', '=', 0);
        }

You have to work it out in some if statements while building up the query.

First pass is a post from a search form, all other passes is a get request.

Aren't you retrieving the parameters from the request, if not, use the network tab in your browser developer tools and see what request and response you are getting.

Did you move paginate, it can go last after all other parts are built up.

And example:

        If (!empty(Request::input('psch'))) {
            $dogsearch = Request::input('psch');
        } else {
            $dogsearch = "";
        }

In your case check for null, and you can use a ternary if also.

public function search(Request $request)
    {
        $query = Products::select('id', 'cats_id', 'brands_id', 'name_ar', 'admins_id')
            ->with('admins:id,name')
            ->with('cats:id,cats_name_ar')
            ->with('brands:id,brands_name_ar');
        if ($request->s !== null) {
            $query->where('name_ar', 'LIKE', "%{$request->s}%");
        }
        if ($request->discount == '1') {
            $query->where('discount', '!=', null);
        }
	$product = $query->paginate(10);
	
	// if sending parameters as array
	$params = [your params array];
	return view('admin.product.indexproduct', compact('product', 'params'));  // if sending params
        return view('admin.product.indexproduct', compact('product'));  //if not sending params
    }

@jlrdw thx pro my last code

    public function search(Request $request){
        $search = Products::select('id', 'cats_id', 'brands_id', 'name_ar', 'admins_id')
            ->with('admins:id,name')
            ->with('cats:id,cats_name_ar')
            ->with('brands:id,brands_name_ar');

        if($request->discount == 1) $search->where('discount', '!=' , null) ? : '';

        $product=$search->paginate(10);
        return view ('admin.product.indexproduct',compact('product'));
    }