Can I sue conversion case?

The question does not explain the time frame involved. Arizona law requires "abandoned" or otherwise leftover personal property to be handled in a certain way, within a certain timeframe. A.R.S. §33-1370 (see link) explains how it is supposed to happen. An eviction judgment almost always comes with a monetary component. The statute addresses that as well. If the landlord did not comply, or some other person disposed of your property independently, you may have a conversion claim. Hopefully the landlord communicated in writing or you made a record of what was said. Your question does not explain what is being appealed or what exactly they want you to release. Are you appealing the eviction judgment? What was the money portion? What is the fair market value of your property? Why did you not remove it once judgment was entered against you? These are all questions that arise from your situation. I recommend you call the Maricopa County Bar Association's Lawyer Referral program. It will give you 30 minutes with a lawyer for $40 or $45.