I believe the 20 years and pay back taxes may be the correct answer, although it got downvoted (and yes, "adverse possession"). For this to work, your use of the land for the 20 years also has to be "notorious", meaning that it's obvious to others that you're using it as your own. For example, you could fence the area that you want to claim. It must also be "hostile", meaning that you were not granted permission to use the land.

It's important to know, though, whether the city (or other municipality) still has claim to the land. I doubt that you can claim the land if the city hasn't relinquished their rights.