How to turn off upgrade message in Umbraco backoffice

for umbraco 8 add add this key in appsettings section in the web.config

<add key="Umbraco.Core.VersionCheckPeriod" value="0" />

https://our.umbraco.com/forum/using-umbraco-and-getting-started/98912-how-to-disable-update-notification-backoffice

Umbraco 9 and Umbraco 10

Add VersionCheckPeriod to the appsettings.json.

{
  "Umbraco": {
    "CMS": {
      "Global": {
        "VersionCheckPeriod": 0
      }
    }
  }
}

When this value is set above 0, the backoffice will check for a new version of Umbraco every 'x' number of days where 'x' is the value defined for this setting. Set this value to 0 to never check for a new version.

References:

• https://our.umbraco.com/Documentation/Reference/Configuration/GlobalSettings/index-v9
• https://our.umbraco.com/Documentation/Reference/Configuration-for-Umbraco-7-and-8/webconfig/

The code for the API controller is also here: https://github.com/umbraco/Umbraco-CMS/blob/e626fca2432582f052cb13654eedd9e60ef8723f/src/Umbraco.Web.BackOffice/Controllers/UpdateCheckController.cs#L47