It's a public thoroughfare (i.e. owned by a government entity, such as the city/town), you can't get ownership of it: there is no mechanism for securing ownership of public land, road, alleys, etc. unless the city, etc. chooses to sell it to you.If it is private land, in *theory* you could get the alley from the current owner after 5 years by adverse possession, but in practice the adverse possession rules will not work for a thoroughfare like an alleyway: that is because under adverse possession, you have to "exclusively" possess the land, but you cannot exclusive possess--i.e. bar other people from--an alley if you get ticketed for even blocking access to it; that is, you clearly cannot bar others from access. The possession must also be "open and notorious," which means it has to be obvous that you are claiming it as your own land and not letting others have access, which means there is no "quiet" way to do this. So in practice, you will not be able to get this alley even if it is private.