month() function and year() function in postgresql through jpa2

Use this: FUNC('MyFunc', a, b, c)

Example: SELECT FUNC('to_char', current_date, 'month')

With JPA criteria API (tested only with Hibernate) :

// Create expressions that extract date parts:
Expression<Integer> year = cb.function("year", Integer.class, date);
Expression<Integer> month = cb.function("month", Integer.class, date);
Expression<Integer> day = cb.function("day", Integer.class, ts);

// Create expressions that extract time parts:
Expression<Integer> hour = cb.function("hour", Integer.class, time);
Expression<Integer> minute = cb.function("minute", Integer.class, time);
Expression<Integer> second = cb.function("second", Integer.class, ts); 

Source : http://www.objectdb.com/java/jpa/query/jpql/date#Date_and_Time_in_Criteria_Queries_

With jpql (tested only with Hibernate) :

YEAR(date)
MONTH(date)
DAY(date) 
HOUR(date)
MINUTE(date)
SECOND(date)

A few examples, how to extract the month from a date or timestamp in PostgreSQL:

select to_char(now(), 'month');
select to_char(now(), 'MM');
select extract('month' from now());
select date_part('month', now());

Just read the manual.