How to use EXECUTE FORMAT ... USING in postgres function

Your function could look like this in Postgres 9.0 or later:

CREATE OR REPLACE FUNCTION dummytest_insert_trigger()
  RETURNS trigger AS
$func$
DECLARE
   v_partition_name text := quote_ident('dummyTest');  -- assign at declaration
BEGIN
   IF NEW.datetime IS NOT NULL THEN
      EXECUTE 
      'INSERT INTO ' || v_partition_name || ' VALUES ($1,$2)'
      USING NEW.id, NEW.datetime;              
   END IF;                    

   RETURN NULL;  -- You sure about this?
END
$func$  LANGUAGE plpgsql;

About RETURN NULL:

• To ignore result in BEFORE TRIGGER of PostgreSQL?

I would advice not to use mixed case identifiers. With format( .. %I ..) or quote_ident(), you'd get a table named "dummyTest", which you'll have to double quote for the rest of its existence. Related:

• Are PostgreSQL column names case-sensitive?

Use lower case instead:

quote_ident('dummytest')

There is really no point in using dynamic SQL with EXECUTE as long as you have a static table name. But that's probably just the simplified example?

You need explicit cast to text:

EXECUTE format('INSERT INTO %I VALUES ($1,$2)'::text ,v_partition_name) using NEW.id,NEW.datetime;