Just extend the class and define $this->modelClass = YourSpecificModel::class;

AbstractRestController.php

<?php
namespace App\Http\Controllers;

use Illuminate\Http\Request;

use App\Http\Requests;

abstract class AbstractRestController extends Controller
{
    protected $modelClass;
    protected $orderBy = 'name';

    public function __construct()
    {
        if (!$this->modelClass) throw new \Exception('Incomplete implementation of AbstractRestController, please define protected $modelClass');
    }

    /**
     * Display a listing of the resource.
     *
     * @return \Illuminate\Http\Response
     */
    public function index()
    {
        $query = \call_user_func([$this->modelClass, 'query']);
        /* @var $query \Illuminate\Database\Eloquent\Builder */
        $resources = $query->orderBy($this->orderBy)->get();
        return response()->json($resources, 200);
    }

    /**
     * Show the form for creating a new resource.
     *
     * @return \Illuminate\Http\Response
     */
    public function create()
    {
        //
    }

    /**
     * Store a newly created resource in storage.
     *
     * @param  \Illuminate\Http\Request  $request
     * @return \Illuminate\Http\Response
     */
    public function store(Request $request)
    {
        //
    }

    /**
     * Display the specified resource.
     *
     * @param  int  $id
     * @return \Illuminate\Http\Response
     */
    public function show($id)
    {
        //
    }

    /**
     * Show the form for editing the specified resource.
     *
     * @param  int  $id
     * @return \Illuminate\Http\Response
     */
    public function edit($id)
    {
        //
    }

    /**
     * Update the specified resource in storage.
     *
     * @param  \Illuminate\Http\Request  $request
     * @param  int  $id
     * @return \Illuminate\Http\Response
     */
    public function update(Request $request, $id)
    {
        $model = \call_user_func([$this->modelClass, 'find'], $id);
        $data = $request->json()->all();
        foreach ($data as $key => $value) {
            $model->{$key} = $value;
        }
        $model->save();
        return response()->json($model, 200);

    }

    /**
     * Remove the specified resource from storage.
     *
     * @param  int  $id
     * @return \Illuminate\Http\Response
     */
    public function destroy($id)
    {
        //
    }
}