We maintain the upkeep on a lot next to our home for the last 13 years, we inquired about purchasing the property years back and the owner agreed to sell to us, but checked further into the property and found out it had a judgement on it, Thank God we didn't give the owner any money yet, since we have keep the property up can we file for Adverse Possession?

I don't think you are using the correct terminology:

www.expertlaw.com/library/real.../adverse_possession

You will have to enter 'adverse possession' in the search in this website to read the entire law.

This isn't what you are looking for in order to claim the property, but if there is a judgment on the properly why would you want it under any circumstances. The judgment would have to discharged by someone, and you don't want that to be you.

... if there is a judgment on the properly why would you want it under any circumstances. [?]

Because, if jimbim could establish title by adverse possession, it would be adverse to the original owner and everyone in privity with him/her, the judgment holder included.

But no, one cannot take another person's property by adverse possession under these circumstances. You need to establish that you possessed the property for all those years "under claim of right". In other words, you need to have thought that the property was yours. I don't see that here.

Where do you live? The true owner has been paying the taxes all along, right?

...You need to establish that you possessed the property for all those years "under claim of right". In other words, you need to have thought that the property was yours. I don't see that here.

A "claim of right" is not required in all states.

I would hire an attorney in your state and have them look at the exact requirements, it may be possible, but even if you meet state requirements, remember not all judges will honor it