Unfortunately, we cannot restrict certain groups of people from downloading the certificate. It might be possible with some custom code to hide the download certificate button from the course congratulation popup and also from the Certifications tab under the Progress tab that is available at the right of the learner dashboard.
Please do note that if the code is applied to the theme of the portal, it will prevent all learners from downloading the certificates.
A workaround if you which to not proceed with the code is that, you may clone the course. In this clone course, you don't need to set up the certificate in the course setting. Thus, you can assign this course to that specific group. However, after completing the course, they will not be awarded a certificate since the certificate is not set up.
We cannot hide the button for specific users only. In case you are interested in this code, please let us know so we can work on it.