JPQL: How to "SELECT new Foo(null, null... someValue, ..)?

You can try (but just a try)

SELECT new Foo(cast(null as string), cast(null as string), f.col3, f.col4)
FROM Foo f

or looking about cast() operator for JPQL if it is supported (I'm not sure)
else

Session session = entityManager.unwrap(Session.class);
List<Foo> list = session.createQuery("select f.col3, f.col4 from Foo f").list()

This is Hibernate specific and you don't need specific constructor for every projections; just create an empty constructor Foo() (at least protected, I don't remember if private is allowed) and let Hibernate inject value into col3, col4 from your query (and cast() operator is supported if your underlying database support the function).

I know this question is old but you can also do (if cast didn't work for you):

String query = "select new Pojo( " +
        " trim(:null), " +
        " trim(:null), " +
        " f.col3, " +
        " f.col4 " +
        " ) " +
        " from Foo as f ";

return em.createQuery(query, Pojo.class)
        .setParameter("null", null)
        .getResultList();

Edited: JPA ignores literal columns when mapping them to the constructor arguments, so wrapped with trim to let JPA aware of the literal value.