Did the city of Ai exist after Joshua destroyed it

No, the city of Ai did not exist after the time of Joshua. In fact it had not even existed for eight centuries before the Bible says that Joshua conquered it, having been abandoned in ruins around 2200 BCE. The very name Ai means ‘Ruins’, the name eventually given to the site by the Hebrew people because they never knew its old name and only ever knew it literally as ruins. Archaeologists say that Ai was not conquered or destroyed by the Israelites. This is supported by evidence that other cities, supposedly conquered by Joshua, were not conquered in a unified invasion in the Late Bronze Age.