Precede the quote character by an escape character (\). : String « Data Types « MySQL Tutorial

mysql>
mysql> CREATE TABLE employee (
    ->      name CHAR(30) NOT NULL
    -> );
Query OK, 0 rows affected (0.03 sec)

mysql>
mysql> INSERT INTO employee (name) VALUES ('\'A');
Query OK, 1 row affected (0.00 sec)

mysql>
mysql> SELECT * FROM employee;
+------+
| name |
+------+
| 'A   |
+------+
1 row in set (0.00 sec)

mysql>
mysql> drop table employee;
Query OK, 0 rows affected (0.00 sec)

mysql>
mysql>

10.21.String
	10.21.1.	Character or String Data Types
	10.21.2.	Strings
	10.21.3.	MySQL recognizes the following escape sequences.
	10.21.4.	To include quote characters within a string
	10.21.5.	A " inside a string quoted with " may be written as "".
	10.21.6.	Precede the quote character by an escape character (\).
	10.21.7.	A single quotation inside a string quoted with double quotation needs no special treatment.
	10.21.8.	A double quotation inside a string quoted with single quotation needs no special treatment.
	10.21.9.	When inserting binary data into a string column (such as a BLOB column), the following characters must be represented by escape sequences:
	10.21.10.	Hexadecimal Values
	10.21.11.	String comparisons normally are case-insensitive