How can I make a filter per user?

You can add a custom constructor that will accept additional parameters:

public ActionResult Backend()
{
  var userId = ....
  return new Dpc(userId).CallBack(this);
}

Dpc class:

public class Dpc : DayPilotCalendar
{
  string userId;

  Dpc(string userId) {
    this.userId = userId;
  }

  // ...
}

You can also set the property value directly.

Another option is to access the controller class using "Controller" property of DayPilotCalendar.

I have included the code you passed me and well I get a message that says the following:
'BackendController.Dpc.Dpc (int)' is not accessible due to its level of protection

How can i fix this?

public class BackendController : Controller
    {
        public ActionResult Day(int idEmpleado)
        {
          
           return new Dpc(idEmpleado).CallBack(this);
        }
    }

class Dpc : DayPilotCalendar
        {
            int userId;
            Dpc(int userId)
            {
                this.userId = userId;
            }
        }

I solved it, it was because I did not put the builder was public. Thank you very much and this question is resolved.