Dawi

This plugin disables the WordPress update notifications, as well as update notifications of different plugins. It is ideal to deliver a complete WordPress and not bother the user with alerts. Silence!
<h4>Please note!</h4>
It’s very important that you keep your WordPress plugins up to date. If you don’t, your blog or website could be susceptible to security vulnerabilities or performance issues. If you use this plugin, you must make sure you keep yourself up to date with new releases of your active plugins and update them as new versions are released.

Silence!

Disables the plugin update checking and notification system.

gr8nilay

This plugin is use to disable all your WordPress core updates as well as notifications for the same. It will prevent your WordPress to check for new updates. This plugin is ideal for whom who have customized and enable theme / plugins to work with existing WordPress verstion and won’t break site at time of WordPress core update.
Read This First: 
You need to keep your WordPress updated including themes and plugins so if you fail for the same then it will might compromise security of your site.

Disable WP Core Updates Advance

Disable all your WordPress core updates on plugin activation.

Silence! vs Disable WP Core Updates Advance