TL;DR:
Update your MySQL version.
I created a simulation of your problem here:
Create table:
CREATE TABLE `turky` (
`id` int(5) NOT NULL AUTO_INCREMENT,
`word` text COLLATE utf8_turkish_ci NOT NULL,
PRIMARY KEY (`id`)
) ENGINE=MyISAM AUTO_INCREMENT=5 DEFAULT CHARSET=utf8 COLLATE=utf8_turkish_ci
Insert data:
INSERT INTO `turky` (`id`, `word`) VALUES
(1, 'axxe'),
(2, 'test word'),
(3, 'axxxxxe'),
(4, 'another test word');
Run test query (that works):
SELECT * FROM `turky` WHERE `word`='axxe'
Result:
1, 'axxe',
Run test query 2 (that works):
SELECT * FROM `turky` WHERE word LIKE '%ax%'
Result:
1, 'axxe',
3, 'axxxxxe',
Run test query 3 (that works):
SELECT * FROM `turky` WHERE word LIKE 'a%'
Result:
1, 'axxe',
3, 'axxxxxe',
4, 'another test word';
Run test query 4 (that does not work originally):
SELECT * FROM `turky` WHERE `word` LIKE 'ax%'
Result:
1, 'axxe',
3, 'axxxxxe',
This works in MySQL, using PHPMyAdmin.
Versions:
MySQL: 5.6.35
PHPMyAdmin: 4.6.6
The current Turkish alphabet doesn't contain the letter "x" so this fact may [probably not] be causing some obscure interference with the SQL sorting process (as in a lack of language guidance when looking for this character).
Web searching Turkish language bugs in MySQL and while there are half a dozen none of them appear to be for your specific instance.
But the only option here that I can see from my own testing (above), using the table and SQL details you've given us, is that you have an older version of MySQL that includes some turkish language bugs.
If your MySQL version is up to date
(or at least, more recent than mine)
Then the issue seems to be specific to your setup and your data, so I highly doubt we can find and reproduce this issue :-(
More Diagnostic stuff:
As commented by Jacob H, see if this issue still occurs after casting to binary:
SELECT * FROM `turky` WHERE BINARY `word` LIKE CONCAT(BINARY 'ax','%');
Result:
1, 'axxe',
3, 'axxxxxe',