I am trying to adopt my nephew from Trinidad West Indies he is currently living in the US with me. I have legal guardianship over him can this be done

There would need to be a lot more information.  Doing an international adoption like this is very difficult because you still have to get parental consent and everything has to comply with New Jersey law.  However, New Jersey law also allows you to adopt an adult, so you can wait until he is 18, and then adopt him.  If you already have legal guardianship, there should be no issue with school, medical care etc.