If your version of Windows has Group Policy Editor, type gpedit in Run box and hit Enter to open it. Navigate to the following setting:
Computer Configuration > Administrative Templates > Windows Components > Internet Explorer > Privacy.
In RHS pane, double-click Turn off InPrivate Browsing, and select Enabled. Click Apply/OK.
This policy setting allows you to turn off the InPrivate Browsing feature. InPrivate Browsing prevents Internet Explorer from storing data about a user’s browsing session. This includes cookies, temporary Internet files, history, and other data. If you enable this policy setting, InPrivate Browsing is turned off. If you disable this policy setting, InPrivate Browsing is available for use. If you do not configure this policy setting, InPrivate Browsing can be turned on or off through the registry.
Alternatively, you could type regedit in Run box and hit Enter to open the Registry Editor. Navigate to the following key:
HKEY_CURRENT_USER\Software\Policies\Microsoft\Internet Explorer\Privacy
Create a new DWORD value and name it EnableInPrivateBrowsing. Set it to 0.
To re-enable InPrivate Browsing, change its value to 1 or delete the EnableInPrivateBrowsing key.
The steps to do this task on Chrome is a little bit difficult. But, it can be done.
policy_templates (the file you’ve downloaded and unzipped) > windows > adm > en-us
Classic Administrative Templates (ADM) > Google > Google Chrome
Now you can see that the incognito mode is gone from Chrome browser. No method will open incognito mode anymore.
If you want the chrome incognito ever, then follow the below steps:
Ref : https://www.technologyhint.com/disable-private-browsing/ & https://www.thewindowsclub.com/disable-private-browsing-internet-explorer-chrome-firefox