Following your father's death in 2014, the house registry is still in his name, despite a will leaving it to you and your mother. You need to update the registry to proceed with constructing a first floor, as required by the Ghaziabad Development Authority. Mutation of property is the correct process to transfer the title in municipal records to your and your mother's names, based on the will. You can initiate this process with the Nagar Nigam by submitting an application with your mother, along with the will, death certificate, and NOC from siblings.