For a specific page, made a custom attribute Authorize and created a RenderMvcController

using System.Web;
using System.Web.Mvc;
using Umbraco.Core.Security;

namespace MyNamespace
{

    public class BackOfficeAuthorize : AuthorizeAttribute
    {

        protected override bool AuthorizeCore(HttpContextBase httpContext)
        {
            bool authorize = true;
            var auth = new HttpContextWrapper(HttpContext.Current).GetUmbracoAuthTicket();
            if (auth == null)
            {
                return false;
            }            

            return authorize;
        }
        protected override void HandleUnauthorizedRequest(AuthorizationContext filterContext)
        {
            filterContext.Result = new HttpUnauthorizedResult();
        }
    }
}

    [BackOfficeAuthorize]
    public class productController : RenderMvcController
    {    
        public override ActionResult Index(RenderModel model)
        {   
            return base.Index(model);
        }
    }

UPDATE: You can also try to use the IsBackOffice attribute

[Umbraco.Web.WebApi.IsBackOffice]
public class productController : RenderMvcController
        {    
            public override ActionResult Index(RenderModel model)
            {   
                return base.Index(model);
            }
        }