I'm a PhD student and I was awarded a fellowship that came to me in my paycheck through the university. This should be tax-free, but since it came into my account through my paycheck, taxes were withheld and it showed up on my W-2. How do I get this money withheld credited back to me and how would I do that in turbo tax?

I suspect that your assumption that the fellowship is tax-free is mistaken. The university payroll departments deal with fellowship income on a routine basis, and they generally know when such income is taxable or tax-free.

Suggest you contact the university payroll department to discuss the matter in detail.