CategoryController.php

<?php

namespace App\Http\Controllers\Api;

use App\Api\ApiMessages;
use App\Category;
use Illuminate\Http\Request;
use App\Http\Controllers\Controller;

class CategoryController extends Controller
{
	/**
	 * @var Category
	 */
	private $category;

	public function __construct(Category $category)
	{
		$this->category = $category;
	}

	/**
	 * Display a listing of the resource.
	 *
	 * @return \Illuminate\Http\Response
	 */
	public function index()
	{
		$category = $this->category->paginate('10');

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

	/**
	 * Store a newly created resource in storage.
	 *
	 * @param  \Illuminate\Http\Request  $request
	 * @return \Illuminate\Http\Response
	 */
	public function store(Request $request)
	{
		$data = $request->all();

		try{

			$category = $this->category->create($data);

			return response()->json([
				'data' => [
					'msg' => 'Categoria cadastrada com sucesso!'
				]
			], 200);

		} catch (\Exception $e) {
			$message = new ApiMessages($e->getMessage());
			return response()->json($message->getMessage(), 401);
		}
	}

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

			$category = $this->category->findOrFail($id);

			return response()->json([
				'data' => $category
			], 200);

		} catch (\Exception $e) {
			$message = new ApiMessages($e->getMessage());
			return response()->json($message->getMessage(), 401);
		}
	}

	/**
	 * Update the specified resource in storage.
	 *
	 * @param  \Illuminate\Http\Request  $request
	 * @param  int  $id
	 * @return \Illuminate\Http\Response
	 */
	public function update(Request $request, $id)
	{
		$data = $request->all();

		try{

			$category = $this->category->findOrFail($id);
			$category->update($data);

			return response()->json([
				'data' => [
					'msg' => 'Categoria atualizada com sucesso!'
				]
			], 200);

		} catch (\Exception $e) {
			$message = new ApiMessages($e->getMessage());
			return response()->json($message->getMessage(), 401);
		}
	}

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

			$category = $this->category->findOrFail($id);
			$category->delete();

			return response()->json([
				'data' => [
					'msg' => 'Categoria removida com sucesso!'
				]
			], 200);

		} catch (\Exception $e) {
			$message = new ApiMessages($e->getMessage());
			return response()->json($message->getMessage(), 401);
		}
	}
}

na linha 44 você esqueceu de tirar a verificação de senha do usuario ... deve ter ocorrido quando você copiou e colou do UserController

Opa @Christian652 obg. Vou fazer a correção.