// Outer query
Root<Task> outerTask = outerQuery.from(Task.class);

// Valid sites for patient (if any)
Set<Site> validSites = ...

// Subquery
Subquery<Task> subquery = query.subquery(Task.class);         
Root<Task> subtask = subquery.correlate(outerTask);
From<Task, Patient> patient = subtask.join(Task_.patient, JoinType.LEFT);
From<Patient, Site> site = patient.join(Patient_.site, JoinType.LEFT);
outerQuery.where(
      builder.exists(subquery
        .select(subtask)
        .where(builder.or(
          builder.isNull(patient.get(Patient_.id)),
          site.in(validSites))))
);

   select
        ... // omitted
   from
        Task task0_ 
    where
       exists (
                select
                    site2_.id 
                from
                    Person patient1_ 
                left outer join
                    Site site2_ 
                        on patient1_.site_id=site2_.id 
                where
                    task0_.patient_id=patient1_.id 
                    and (
                        patient1_.id is null 
                        or site2_.id in (
                            ?
                        )
                    )
            )
    )