You can filter the posts list by appending ?category_name=xx
to the admin posts list URL, and you can add a submenu page with that URL as the target via add_submenu_page
:
add_action( 'admin_menu', 'wpd_admin_menu_item' );
function wpd_admin_menu_item(){
add_submenu_page(
'edit.php',
'Page title',
'Menu item title',
'edit_posts',
'edit.php?category_name=somecat'
);
}