Q:

Is there a way to return Specifications for Parent Entity for org.springframework.data.jpa.domain. Specification? 

Suppose I have a bidirectional 1-1 association with the Person entity
@Entity
public class Person {
  @OneToOne(optional=false)
  @JoinColumn(name = "contact_id")
  private Contact contact;

  // getters/setters/constructors
}

And the Contact Entity
@Entity
public class Contact {
  @OneToOne(mappedBy="contact")
  private Person person;

  // getters/setters/
}

I couldn't find a way to select parent object for Person Entity using the Contact entity.  Like so...
criteriaQuery.select(root.get(Contact_.person));

I get this error:
Incompatible types.  Required Selection<?  extends capture of ? > but 'get' was inferred to Path<Y>: no instance(s) of type variable(s) exist so that Person conforms to capture of ? 
Is there a way of doing this?  I wanted to return a Predicate for Person Entity using the Contact root.  For eg. 
public static Specification<Person> phoneWithCountryCode(String countryCode) {
    return new Specification<Person>() {
        @Override
        public Predicate toPredicate(
            Root<Contact> root,
            CriteriaQuery<? > criteriaQuery,
            CriteriaBuilder criteriaBuilder
        ) {
            String startsWithPattern = countryCode + "%";
            criteriaQuery.select(root.get(Contact_.person));
            return criteriaBuilder.like(
                root.get(Contact_.phone), startsWithPattern
            );
        }
    };
}

A:

Yes, you can do. 
I did it. I Have Relationship ( Book -- Review). 
In your case create Specification<Person> and use join with contact. 
like this,
Join joins = root.join("contact");

If help requires just follow my code. 
public class BookSpecification {

    public static Specification<Book> getBookByNameAndReviewId(){

        return new Specification<Book> () {

            @Override
            public Predicate toPredicate(Root<Book> root, CriteriaQuery<? > query, CriteriaBuilder cb) 
            {
             //List<javax.persistence.criteria. Predicate>
            List<Predicate> predicates = new ArrayList<>();
            predicates.add(cb.equal(root.get("name"), "spring boot"));
            Join joins = root.join("reviews");
            predicates.add(cb.equal(joins.get("no") , 584));

                return cb.and(predicates.toArray(new Predicate[predicates.size()]));
            // return cb.equal(root, predicates);
            }

        };
    }
}

