function my_kboard_list_from($from, $board_id, $content_list){
    if($board_id == '10'){
        global $wpdb;
        $from = "`{$wpdb->prefix}kboard_board_content` LEFT JOIN `{$wpdb->prefix}kboard_board_option` ON `{$wpdb->prefix}kboard_board_content`.`uid`=`{$wpdb->prefix}kboard_board_option`.`content_uid`";
    }
    return $from;
}
add_filter('kboard_list_from', 'my_kboard_list_from', 10, 3);

function my_kboard_list_where($where, $board_id, $content_list){
    if($board_id == '10'){
        global $wpdb;
        $meta_key = 'addinfo4';
        $where .= " AND (`option_key`='{$meta_key}' )";
    }
    return $where;
}
add_filter('kboard_list_where', 'my_kboard_list_where', 10, 3);

function my_kboard_list_orderby($order, $board_id, $content_list){
    if($board_id == '10'){
        global $wpdb;
        $order = "`{$wpdb->prefix}kboard_board_option`.`option_value` DESC";
    }
    return $order;
}
add_filter('kboard_list_orderby', 'my_kboard_list_orderby', 10, 3);

<form id="kboard-search-form-<?php echo $board->id?>" class="form-row" method="get" action="<?php echo esc_url($url->toString())?>">
            <?php echo $url->set('pageid', '1')->set('target', '')->set('keyword', '')->set('mod', 'list')->toInput()?>
            <select name="target" style="display: none">
                <option value=""><?php echo __('All', 'kboard')?></option>
                <option value="title"<?php if(kboard_target() == 'title'):?> selected<?php endif?>><?php echo __('Title', 'kboard')?></option>
                <option value="content"<?php if(kboard_target() == 'content'):?> selected<?php endif?>><?php echo __('Content', 'kboard')?></option>
                <option value="member_display"<?php if(kboard_target() == 'member_display'):?> selected<?php endif?>><?php echo __('Author', 'kboard')?></option>
                <option value="kboard_option_addinfo4" <?php if(kboard_target() == 'kboard_option_addinfo4'):?> selected<?php endif?>>옵션1</option>
                <option value="kboard_option_addinfo3" <?php if(kboard_target() == 'kboard_option_addinfo3'):?> selected<?php endif?>>옵션2</option>
            </select>
            <div class="col"><input type="text" name="keyword" class="form-control" value="<?php echo esc_attr(kboard_keyword())?>" placeholder="검색어를 입력해주세요"></div>
            <div class="col-auto"><button type="submit" class="btn btn-primary"><i class="icon-search">search</i></button></div>
        </form>

<option value="kboard_option_addinfo4" <?php if(kboard_target() == 'kboard_option_addinfo4'):?> selected<?php endif?>>옵션1</option>
<option value="kboard_option_addinfo3" <?php if(kboard_target() == 'kboard_option_addinfo3'):?> selected<?php endif?>>옵션2</option>