$res02=mysql_query("SELECT * FROM `verify` ORDER BY rand() AND `text` IN ('$_SESSION[ver]') LIMIT 3");

$res02=mysql_query("SELECT * FROM (SELECT * FROM `verify` WHERE `text` NOT IN ('$_SESSION[ver]')) ORDER BY rand() LIMIT 3");

<?php
session_start();
require_once '../sys/mysql.php';
$res01=mysql_query("SELECT * FROM verify order by rand() LIMIT 1");
$res001=  mysql_fetch_assoc($res01);
$_SESSION[ver]=$res001[text];
echo 'Выберите картинку, соответствующую признаку <b>'.$res001[text].'</b><br>';

$res02=mysql_query("SELECT * FROM `verify` ORDER BY rand() AND `text` IN ('$_SESSION[ver]') LIMIT 3");
echo '<form action="verify.php" method="POST">
    <div style="display: none;"><input checked type="radio" value="agree" name="ver[]"></div>
    <input type="radio" name="ver[]"><img src="images/verify/'.$res001[name].'.png">
        
';

while ($res002=  mysql_fetch_assoc($res02)) {
    echo '<input type="radio" name="ver[]"><img src="images/verify/'.$res002[name].'.png">';
}
    

?>

$row=mysql_fetch_array($res);

<?php
session_start();
require_once '../sys/mysql.php';
$a=0;
$n=4;
$r=rand(0,$n);
echo '<form action="verify.php" method="POST">
      <div style="display: none;">
      <input checked type="radio" value="agree" name="ver[q]"></div>';
$res=mysql_query("SELECT * FROM verify order by rand() LIMIT $n");
while($rst=mysql_fetch_assoc($res)){
   if($r==$a++) {
	$_SESSION[ver]=$rst[text];
	echo 'Выберите картинку, соответствующую признаку <b>'.$rst[text].'</b><br>';
   }
echo '<input type="radio" name="ver[q]" value="$rst[text]">
<img src="images/verify/'.$rst[name].'.png">';
}
?>

while($rst=mysql_fetch_assoc($res)){
   if($r==$a++) {
	$_SESSION[ver]=$rst[id];
	echo 'Выберите картинку, соответствующую признаку <b>'.$rst[text].'</b><br>';
   }
echo '<input type="radio" name="ver[q]" value="$rst[id]">
<img src="images/verify/'.$rst[name].'.png">';
}

$res02=mysql_query("SELECT * FROM  `verify` WHERE `text`!='$_SESSION[ver]' ORDER BY rand() LIMIT 4");