Hello there, domicile certificate is a document for recognition of a person's residential status in a state. To have the domicile of  a particular state one needs to own a house, property or land in that particular state.

I would suggest you to look for the address mentioned on your birth certification and also of your father's birth certificate and other documents like driving license or Aadhar card.  Generally, that will be the address considered by the authorities for providing you domicile certificate.

And incase you want to apply for domicile of UP, kindly visit the municipal board and talk to the authorities for a TRC (Temporary Resident Certificate). Your rent agreement can serve as a document for applying TRC. And once you have the TRC, you can apply for PRC (Permanent Resident Certificate).

Hope this helped.

Thank you.