How to insert multiple values in a specific field in a table using mysqli?
No.  Don't put multiple values in a column; make a new table:

Mapping table
-id -- same as the `id` in transaction_tbl
-ref_number
PRIMARY KEY(id, ref_number)


For your example, there will be 3 rows in this table for the 1 row in transaction_tbl.

INSERT INTO transaction_tbl (name, descripton) VALUES (..., ...)
$id = LAST_INSERT_ID()
INSERT INTO mapping (id, ref_number) VALUE ($id, '10359435846')
INSERT INTO mapping (id, ref_number) VALUE ($id, '05438547656')
INSERT INTO mapping (id, ref_number) VALUE ($id, '035848576')


One way of getting the output:

SELECT t.id, t.name, t.description,
       GROUP_CONCAT(m.ref_number) AS ref_numbers
    FROM transaction_tbl t
    JOIN mapping m  ON m.id = t.id
    GROUP BY t.id;