If using “regular” query in theme file (sidebar.php for example), this code will help do the trick:
<?php wp_get_archives('type=monthly&limit=12'); ?>
The above (and below) will only show the last 12 months.
However if using a widget, then add this code to your functions.php file:
function my_limit_archives( $args ) {
$args['limit'] = 12;
return $args;
}
add_filter( 'widget_archives_args', 'my_limit_archives' );
add_filter( 'widget_archives_dropdown_args', 'my_limit_archives' );
Note: In both of the above code examples, I don’t remember where I got the original code from (Google can probably find it?). I just pulled this from a fix I effected on another theme.
Finally, this resource may help point you in the direction to list archives only from 2010 to the present: http://www.wpbeginner.com/wp-themes/how-to-customize-the-display-of-wordpress-archives-in-your-sidebar/
I hope the above helps you in some way! 🙂