Hi Jatin,
It doesn't take much time to get your domicile, usually around a week. If you don't submit a copy of it during counseling, you will be considered an outsider and you might not get your desired college.
I'd suggest you to keep looking at UPSEE's websites for dates. Below is the link for the same
https://upsee.nic.in/publicinfo/public/home.aspx
All the best.
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