저 is for people that are higher than you or for formal situations.
나 is for people that are lower than you or for people that have agreed to let you speak intimately with them.
But you would say it like this:
저는 학생이에요
나는 학생이야
Note:
Maybe you've seen 저는 학생입니다. This sounds like a formal situation (like a self-introduction in front of a group) and not like a friendly conversation.
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저 is used when talking to people who are older than you and/or have a higher status (e.g your boss)
나 is used with your friends of the same age and with younger people.
Some possible variants of your sentence are:
저는 학생입니다
저는/나는 학생이에요
나는 학생이야
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I think "나는 학생 니다" is informal and "저는 학냉 아애요" is formal, so both sentences are right but they have different level of politeness, but I'm not sure