The nurse should absolutely not harshly dismiss the patient's fears right off the bat by saying anything like "no they aren't" or "you're being ridiculous", because that will only ingrain the fear further into the patient's head, and they will begin to believe that they can't trust the nurse either.
First of all, you need to realize that the fact that the patient is even saying anything about this is progress. That means that they trust you enough or are recovered enough to not be paranoid of you too, and you can't break that. Whatever you do, don't begin to argue with the patient about their fears. It doesn't matter if you think it's valid or not. To them, it absolutely is.
The second step is to help the patient focus on something that's real. Ask them why they think so. Ask them if anything has happened to make them believe this. Get them talking, and slowly let them come to the realization that they are safe and no harm will come to them. Safety is a big thing for people with paranoid schizophrenia. This also includes giving them enough space so they don't feel cornered and telling them what you're going to do before you do it so you don't startle them: i.e. "I'm going to walk over here now."
Third step is, if there is a specific cause for this feeling, get the patient away from whatever is causing it.
And most of all, if the patient is threatening you, himself, or others, call for help.
