Information collection is a big business these days. Most entities, like SearchQuarry, utilize public records searches to acquire information about you. The specific records used by any given entity are known only to that entity. However, if you are receiving information about yourself that is not true, your first step should be to contact the provider and then to file a complaint with the FTC by going to ftc.gov/complaint, or here: https://www.ftccomplaintassistant.gov/#crnt&panel1-1. The next step would be to contact your state attorney general, as they perform on the state level a similar consumer protection function to the FTC. You should also check your credit reports with Experian, Equifax, and TransUnion to see if your credit history files have been accessed.
As far as taking legal action, you should go back to the SearchQuarry agreement and read it carefully, because it most likely will contain a hold harmless clause stating that they are not responsible for the accuracy of information obtained from third party sources. To prevail in a lawsuit you would have to demonstrate that they should have known the information was inaccurate yet they charged you for it and provided it anyway.
To begin, you should write to SearchQuarry and tell them what happened. That will document your experience, put them on notice, and hopefully provoke some type of response from them that will lead to further investigation. I do not recommend trying to communicate with them by phone because you don't know who you're speaking with and despite what they might tell you, they can always deny it later. Make sure you get everything in writing!
Finally: to say that information came from "the state" is nebulous at best. Most states have public records laws giving citizens the right to access public information. Theoretically, you should be able to access all of the information provided by SearchQuarry. Civil and criminal court records, voter registration records, property ownership records, the list is virtually endless. So if I were you, I'd begin with a very specific letter to SearchQuarry that tells them they've provided false information, and then follow up with the FTC and AG. Oh, one more thing. This is a slow process. Be patient. We miss things when we hurry.