$sql = "select foo from bar where catid = $cat limit 20";
$result = mysql_query($sql ,$db);

$scriptoutput = '';
while ($myrow = mysql_fetch_array($result))
{
    $scriptoutput .= '<li>' . $myrow['something'];
}

$myfile= fopen ("/home/domains/domain.com/public_html/mytxt.txt", "w+");
fwrite($myfile, $scriptoutput);
fclose($myfile;

$mysqli = new mysql( 'localhost', 'username', 'password', 'db' );

$content = '';
if( $stmt = $mysqli->prepare("SELECT foo FROM bar WHERE catid = ? LIMIT 20") ) 
{
  $stmt->bind_param( 'i', $cat );
  $stmt->execute();
  $stmt->bind_result( $foo );
  while ( $stmt->fetch() )
  {
    $content .= '<li>' . $foo;
  }
  $stmt->close();
}

$mysqli->close();

file_put_contents( '/path/to/saved.txt', $content );