I have two DDs with autism. Both high functioning, academically able, articulate and anxious.
Both have had times when their anxiety was unmanageable and they lost it a lot. This has usually been due to inappropriate school provision or big changes to routine. Things have always got better once the problem has been sorted out. It really helps us to have firm, regular school holiday plans in place with a daily routine that stays pretty much the same for the mornings at least.
I am not an advocate of giving a child anything because they are screaming and being aggressive. This is never going to be a good idea.
However, you need to think about why he is so desperate to have this screen time.
My DDs use screens to calm down. Screens impose no social demands, they can be very predictable, especially if you watch the same thing over and over, and they put the child in control. This makes them a great tool for managing anxiety.
So, if your son is having a tough time, perhaps because of a demanding day or maybe because he is missing the routine of school, ask yourself if you could build this time into his evening in the future to help him feel calmer.
If you don't want him to have the screen time, can you find other strategies to help him feel calmer? Weighted objects, walks, familiar stories, bath time, etc.