You do need a real estate attorney to evaluate your specific facts and the history of the fenced in area. Since you just bought the property, if you are going to pursue adverse possession, you will need to have proof of the last 10 years of use of the area. Since it is a "repo", by which I think you mean a foreclosure, you may not have much cooperation from the immediately prior owner(s) being the bank and the person foreclosed upon. You might be able to get proof of when the fence was put in on your own. If your legal description of what you bought does not cover the area in question, then you need to either pursue adverse possession or a purchase of the property from whoever owns it, which could be its own legal issue if the county does not show your neighbor as the owner. This is a situation where you do need an attorney to be able to get the right answers and take the steps necessary to quiet title.
Disclaimer: This answer is provided for informational purposes only, does not constitute legal advice, and does not create an attorney-client relationship. I am licensed in Arizona and can only provide general comments on matters outside of Arizona law. Actual legal advice can only be provided after a direct consultation in which all of the relevant facts are considered before providing a response.
Have the property surveyed. If your survey agrees with your assumption, I suggest you hire counsel.
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In the state of Arizona, a person may claim adverse possession if he actually enters the property, makes his possession of the land visible to the public and exclusively possesses the land without the owner’s consent. Possession of the property must be continuous for at least 10 years; a person who occasionally possesses a property when he is not the legal owner may be considered a trespasser in violation of law and has no right to an adverse possession.
Arizona law states that a person may meet the requirement for 10 years of continuous possession through tacking. Tacking occurs where there are successive adverse possessors who each possess the property for less than 10 years but 10 years in aggregate. If a person is in adverse possession of a property for four years and then sells it to another person, who takes adverse possession of the property for six years, then the current person in adverse possession of the property may tack his successor's four years of possession onto his six years of possession to meet Arizona’s 10 years of continuous possession requirement.
Specific to your situation, you should see counsel and determine the date of entry ans well as whether the prior owner had continuous or periodic use.
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