1. He is the student of our school.
2. He is the only student of our school.
[Does #1 mean #2? Does #1 mean that there is only one student in our school?]
3. They are some students of our school.
4. They are students of our school.
[Does #3 mean #4? Are both used commonly?]
Not "of our school" -- please use "at" or "in" our school.
1. He is the student at our school.
2. He is the only student at our school.
[Does #1 mean #2? Does #1 mean that there is only one student in our school?] Yes
3. They are some of the students at our school.
4. They are students at our school.
[Does #3 mean #4? Are both used commonly?] I changed a bit of the phrasing so please read and reread them to be aware. 3 and 4 are very close to meaning the same thing.