Based on the question, I am assuming these are online quizzes in Canvas. If so, the only way I could think of that would be using something like respondus lockdown browser with monitor(especially if they are remote and not in a class room). I am assuming that lockdown browser would prevent the screenshot capability. and monitor for remote students would allow you to catch them using their phone to take a picture.
Note - I just mentioned respondus because that is what I have heard of. I imagine there are other similar products.
Do you have access to any products such as Respondus LockDown Browser, ProctorU, or other similar software at your institution? Those are the only products that I am aware of that can lock students into their exams and prevent them from getting screenshots.