Hello dear student,
No that would not be a problem. You must have a domicile of UP that's all you need. The address of adhar card doesn't matter. As it consists of your current address and it's not the proof of your domicile. While here is the eligibility criteria:
I hope this was helpful while here I am attaching a link that might help your more to clear your doubts .. https://www.google.com/amp/s/engineering.careers360.com/articles/upsee-eligibility-criteria/amp
Thank you
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