properly set search_path in cluster, database, role, session, function level.

set_search_path.sql

--https://stackoverflow.com/questions/9067335/how-does-the-search-path-influence-identifier-resolution-and-the-current-schema/9067777#9067777
--properly set search path.
--Set it in cluster level.
ALTER SYSTEM SET search_path TO 'public';
SELECT pg_reload_conf();

--Set it as default for database test16.
ALTER DATABASE test16 SET search_path = '$user', 'public';

-- Set it as default for the role (bob) you connect with (effective cluster-wide):
ALTER ROLE bob SET search_path = '$user', 'public';

--Set as default for a role(bob) in a database (test16).
ALTER ROLE bob IN DATABASE test16 SET search_path = '$user', 'public';

--Set it in a session level.
SET search_path = '$user', 'public';

--set it for the function.
CREATE OR REPLACE FUNCTION test_search_path ()
    RETURNS void
    LANGUAGE plpgsql
    SECURITY DEFINER
    SET search_path = new, public, pg_temp
    AS $fun$
BEGIN
    --query part
END
$fun$;