At the class quizzes or at the mid- or final exams, I can see that some students are too anxious and nervous. They are not really weak students but too much anxiousness brings their efficiency down and they even may fail their important exams. In one of our important exams I could see that a student was that much nervous that he could not really sit on his chair, another one was so sick that needed to go to the bathroom or see a doctor. This may happen once per year but seeing such uncomfortable students is so sad. I really feel that I have to help them as I am their teaching-assistant.
As a teaching-assistant, when I see that there are one or two nervous students at my class; if they feel they need to consult about their anxiety I try to calm them down before the exam by talking to them privately after the class and if they are good students, remind them that they are perfect students and should not allow nervousness to ruin their exam's mark; and explain their academic potentials and their perfect progress to the professor. Of course I don't have any knowledge about anxiety, so I don't talk about their nervousness problems and I ask them to see a doctor who can help them. I only try to talk and help them about their problems in the course I am teaching. If the student has not good academic progress and I see that his anxiety is because of his academic performance, I spend more time for them answering their questions in the office hours when I am at the university.
At the exam session, when I see such students; If they need and ask for something to eat to relieve their anxiety I try to bring them bottle of water and sugar to help them feel more comfortable and answer their questions more relaxed.
However, I can not really give them extra time to solve their questions as it may be not fair to other students sitting the same exam or help them giving some clues over questions. Also, I can not give them some extra mark because of their nervousness because I think it is not fair at all.
As lecturers, teachers or even TAs who may have experience about this; could you please share me your experience and what you did about such anxious students?
What do you do about such nervous students to calm down and feel better at the exam session?