How many bytes does character takes if I created database with utf8 in mysql Suppose if create a database with utf8 character set and created table and inserted data. 
Here my doubt is if the character is 1 byte then  it will occupy only 1 byte or it will occupy 3 bytes because of utf8 character set
Depends on a character. Some need one byte, some - four. See http://www.fileformat.info/info/charset/UTF-8/list.htm .
MySQL has two UFT8 character sets:

mysql&gt; SHOW CHARACTER SET like 'UTF8%';
+---------+---------------+--------------------+--------+
| Charset | Description   | Default collation  | Maxlen |
+---------+---------------+--------------------+--------+
| utf8    | UTF-8 Unicode | utf8_general_ci    |      3 |
| utf8mb4 | UTF-8 Unicode | utf8mb4_general_ci |      4 |
+---------+---------------+--------------------+--------+
2 rows in set (0.01 sec)


If a character is a one byte, it will use one byte in memory and on a disk. If four - then four. Plus the string will use one or two bytes to encode length of the string.
Note, that utf8 character set cannot encode all UTF8 characters.