1. I am Bora, your student last year.
2. I am Bora, your student from last year.
3. I am Bora, your student who is from last year.
(Are all correct? In #2, what does 'from last year' modify? What is the part fo speech of 'from last year'?)
Only #2 is correct and smoothly worded. The prepositional phrase "from last year" serves as an adjective, modifying "student."
from = preposition
last = adjective, modifying "year"
year = noun, object of the preposition "from"
(from last year) preposition phrase