Check out the default comment-template.php file:
wp-includes/comment-template.php
You will need to replace the arguments:
$defaults = array(
'fields' => apply_filters( 'comment_form_default_fields', $fields ),
'comment_field' => '<p class="comment-form-comment"><label for="comment">' . _x( 'Comment', 'noun' ) . '</label><textarea id="comment" name="comment" cols="45" rows="8" aria-required="true"></textarea></p>',
'must_log_in' => '<p class="must-log-in">' . sprintf( __( 'You must be <a href="https://wordpress.stackexchange.com/questions/174775/%s">logged in</a> to post a comment.' ), wp_login_url( apply_filters( 'the_permalink', get_permalink( $post_id ) ) ) ) . '</p>',
'logged_in_as' => '<p class="logged-in-as">' . sprintf( __( 'Logged in as <a href="%1$s">%2$s</a>. <a href="%3$s" title="Log out of this account">Log out?</a>' ), admin_url( 'profile.php' ), $user_identity, wp_logout_url( apply_filters( 'the_permalink', get_permalink( $post_id ) ) ) ) . '</p>',
'comment_notes_before' => '<p class="comment-notes">' . __( 'Your email address will not be published.' ) . ( $req ? $required_text : '' ) . '</p>',
'comment_notes_after' => '<p class="form-allowed-tags">' . sprintf( __( 'You may use these <abbr title="HyperText Markup Language">HTML</abbr> tags and attributes: %s' ), ' <code>' . allowed_tags() . '</code>' ) . '</p>',
'id_form' => 'commentform',
'id_submit' => 'submit',
'title_reply' => __( 'Leave a Reply' ),
'title_reply_to' => __( 'Leave a Reply to %s' ),
'cancel_reply_link' => __( 'Cancel reply' ),
'label_submit' => __( 'Post Comment' ),
);
Override the part of the form where you want to insert your required item. For example, I use the after_notes section as follows normally:
$defaults['comment_notes_after'] .= '<div>Your Code Here</div>';
You can then call comment form like:
comment_form( $defaults );
That should draw your extra section into the comment form.
The simplest way to do this would be to add your content to the comment_notes_after argument on the comment form.
For example:
$comment_fields = array(
'comment_notes_after' => '<p class="form-allowed-tags">' . sprintf( __( 'You may use these <abbr title="HyperText Markup Language">HTML</abbr> tags and attributes: %s' ), ' <code>' . allowed_tags() . '</code>' ) . '</p><p>Enter Code:<input name="security" value="" /></p>';
);
apply_filters( 'comment_form_default_fields', $comment_fields );
That should add <p>Enter Code: <input name="security" value="" /></p> after the allowed fields section of the comment form.
It needs the first part as that is what is in the comment_notes_after field by default.