How to handle bonus payback taxes and a new job with 1040-ES?

Last year, I started a new job that had a sign-on bonus requiring 2 years at the company. A couple months ago, I left that job just before a year of being there to take a fellowship position. Upon leaving my previous job, I had to pay back the proportionate amount of that sign-on bonus, including the amount that had already been withheld for taxes by the company.

I have seen a few questions on here regarding how to get back the taxes on the repayment and have an idea of how to do that (deduction since the amount is under $3000). However, with my fellowship position, I have to do estimated taxes. 

My question is, is there a way for me to utilize that deduction for my estimated quarterly taxes? Meaning, since ~$3000 is owed back to me, do I need to make quarterly tax payments? 

I was planning on just making quarterly payments and waiting until my tax refund for everything to even out, but if there is a way to handle it now that would be great. 


Please let me know your thoughts, and if you need any clarification!