PostgreSQL – Conditional WHERE for Stored Procedure

I want to create a conditional where clause using a PostgreSQL stored procedure.

This is my original stored procedure :

    select distinct 
    t.serialnumber as sn, 
    t.productid as tid,  
    t.merchantid as mid  
    from tbterminal as t
    ORDER BY idterminal ASC 

I want to check if p_mid, p_tid and p_sn are null or empty; if not null and not empty, add an and where for every component.

This is what I've tried :

CREATE OR REPLACE FUNCTION get_list_terminal_datatable (
    p_mid varchar, 
    p_tid varchar,
    p_sn varchar,
    p_limit int, 
    p_offset int
) 
 RETURNS TABLE (
 sn VARCHAR,
     tid varchar,
     mid varchar
) 
AS $$
DECLARE
  data_where varchar := 'WHERE ';
BEGIN

 IF p_mid notnull and p_mid != '' THEN
   data_where := data_where || ' t.merchantid like '''%|| p_mid ||'%'' ';
 END IF;
 IF p_tid notnull and p_tid != '' THEN
   data_where := data_where || ' t.productid like '''%|| p_tid ||'%'' ';
 END IF;
 IF p_sn notnull and p_sn != '' THEN
   data_where := data_where || ' t.serialnumber like '''%|| p_sn ||'%'' ';
 END IF;
 RETURN QUERY 
 select distinct 
    t.serialnumber as sn, 
    t.productid as tid,  
    t.merchantid as mid  
    from tbterminal as t
    ORDER BY idterminal ASC 
    limit p_limit offset p_offset;
END; $$ 

LANGUAGE 'plpgsql';

I know it doesn't work properly, so I need help on how to make the conditional where clause stored procedure in PostgreSQL work.

How would I have to write the stored procedure correctly?