Someone has done black magic on our family to break it up and we are doing everything to stop it but my question is, is it really true that the shaytaan and evil jinn are locked up in Ramadhan? If so, then does that lower the effect of black magic in the month of Ramadan?

Yes we have hadiths that they are locked up in Ramadhan. It doesn’t mean they cannot influence us, but their influence decreases, and there are less opportunities for many Muslims to sin in Ramadhan compared to other months