On Netcore email API panel, you can make use of suppression feature available on Netcore email API panel to blacklist/suppress a user. In order to use the suppression option, you can follow the below steps,

1. Login to your Netcore email API panel, URL: https://email.netcorecloud.com
2. Go to suppression as shown under below image,

3. Click on manage suppression as shown below,

Once done, you get an option to add or remove an email address from suppression. Here you can either suppress an individual email address or upload a CSV of users to suppress them or to whitelist them on your Netcore email API account.

Please refer to the image below for more information,

Hope this helps.