Can a city force you to get a building permit for something that has been existing prior to u buying the home?

It could be that the patio was not there when the house was last appraised buy the city. If you do not get the permit, they can make you tear it down. It could be that you can make the seller pay for the permit. There might also be a "grandfather" clause you can slid in under. They do this to make money, bottom line.