If anything, SIXTH-year student, but that's not really idiomatic unless you're talking about university, and even then sounds a bit rough as a general fact.

https://books.google.com/ngrams/graph?content=six+year+school+student%2Csixth-grade+student%2Cin+sixth+grade%2Csixth-year+student%2C+year+six+school+student&corpus=26&year_end=2019&year_start=1800&smoothing=3&direct_url=t1%3B%2Csixth%20-%20grade%20student%3B%2Cc0%3B.t1%3B%2Cin%20sixth%20grade%3B%2Cc0%3B.t1%3B%2Csixth%20-%20year%20student%3B%2Cc0

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