trogau

You can query core, plugin, and themes individually, or check all at once.
It defines four new methods:
<ul>
<li>xmlrpcCoreUpdateCheck – checks core, returns true/false</li>
<li>xmlrpcPluginUpdateCheck – checks plugins, returns true/false</li>
<li>xmlrpcThemeUpdateCheck – checks themes, returns true/false</li>
<li>xmlrpcUpdatesCheck – checks all of the above, returns an array of trues/falses.</li>
</ul>
The plugin was created primarily for WPUpCheck (http://trog.qgl.org/wpupcheck/), a simple 
Windows application that remotely polls a WordPress site to see if updates are available.

XML-RPC Update Check

This plugin provides XML-RPC methods for checking the update status of WordPress websites.

Scott Reilly

This plugin removes the WordPress update nag that appears at the top of all admin pages when a new version of WordPress is released.
Tired of WordPress nagging you about a new release? Maybe you already know about it and want to hold off on an update and would rather not see the update nag on every admin page you visit. Activate this plugin and be bothered no more!
The status of your version of WordPress (be it current or out-of-date) is still reflected in the footer of your admin pages and in the update count link in the admin bar.
And certainly, of course, I don’t advocate completely ignoring the fact that updates often contain fixes for critical bugs or exploits. However, there are various other means of learning about updates; and once known, not everyone is able or willing to update immediately.
Links: <a href="https://coffee2code.com/wp-plugins/no-update-nag" rel="nofollow ugc">Plugin Homepage</a> | <a href="https://wordpress.org/plugins/no-update-nag/" rel="ugc">Plugin Directory Page</a> | <a href="https://github.com/coffee2code/no-update-nag/" rel="nofollow ugc">GitHub</a> | <a href="https://coffee2code.com" rel="nofollow ugc">Author Homepage</a>

No Update Nag

does what it says on the tin

Removes the WordPress update nag that appears at the top of all admin pages when a new version of WordPress is released.

XML-RPC Update Check vs No Update Nag