There seems to be a problem with "else if", I think it needs to look like this:
CREATE FUNCTION public.test1(IN p_col1 integer, IN p_col2 text, IN p_col3 text) RETURNS void AS
$BODY$begin
if(p_col2='1') then
UPDATE tblA set COLUMN12=p_col3 WHERE COLUMN0=p_col1;
end if;
if (p_col2='2') then
UPDATE tblI set COLUMN11=p_col3 WHERE COLUMN0=p_col1;
end if;
end;
$BODY$
LANGUAGE plpgsql;