create drop down menu in theme customizer from custom db

Assuming that you mean that students is a table within your WP database, this should get you started.

I’d recommend a read of the following materials, which are pretty useful –

• WordPress Codex for $wpdb.
• WordPress Codex for Theme Customization API.

Here is the code to add the dorpdown box –

/** Required to make use of the wpdb Class */
global $wpdb;

/** Query the database */
$query = $wpdb->prepare('SELECT * FROM %1$s ORDER BY ID DESC', 'students');
$results = $wpdb->get_results($query);

/** Check for $results */
if(!empty($results)) :

    /** Loop through the $results and add each as a dropdown option */
    $options="";
    foreach($results as $result) :

        $options.= sprintf("\t".'<option value="%1$s">%2$s</option>'."\n", $result->ID, $result->name);

    endforeach;

    /** Output the dropdown */
    echo '<select id="my-select" name="my-select">'."\n";
    echo $options;
    echo '</select>'."\n\n";

endif;