Some of my users are getting a pop up "windows security Microsoft outlook"

Outlook app. part of the 365 suite

Dear Jorge C enterprise,

Thanks for choosing Microsoft Community.

Based on your description, I know the scenario you met. First, if you do not want this to remember credentials, for this, the users need to remove credentials first and then when this window pop up, do not choose remember the crendients. And for remove this, please check the following：

1. Click Start, click Control Panel, and then click Credential Manager.
   Note If View by is set to Category, click User Accounts first, and then click Credential Manager
2. Locate the set of credentials that has Outlook in the name.
3. Click the name to expand the set of credentials, and then click Remove from Vault.
4. Repeat step 3 for any additional sets of credentials that have the word Outlook in the name.

And for  "windows security Microsoft outlook", from your description, some users in your organization are having the same issue when using Outlook. May I confirm if your organization has enabled multi-factor authentication (MFA) for these users? 

If so, please also make sure your admin has enabled Modern Authentication for Outlook in the Microsoft 365 admin center > Settings > Org settings > Modern Authentication > make sure to enable the option “Turn on modern authentication". 

Also, you may ask affected users to download Microsoft Support and Recovery Assistant (SaRA) and try the option "Outlook keeps asking for my password“ to see if it helps.   

If SaRA cannot help to fix this issue, to further narrow down this issue, we need to collect following information in private message:

1. A screenshoot of problematic Outlook client version in File > Office Account.
2. A screenshoot of the Windows security popup.
3. Did your organization make any changes before this issue happens?

Below are the steps to open private message:

• To View private messages option > click on Profile Picture at top of the right side > Select My Profile option.

Thanks for your precious time. Have a nice day.

Sincerely,

Katherine

Are you using Outlook app or a browser to access the mailbox?

Where would i find the version, it's on the microsft exchange server

Which Outlook version are you using? Where is the mailbox hosted (365?)?