If I were you, I would write a letter to the collection agency which explains that you believe that the debt was paid, and that you dispute the debt and want it verified, and that you want a statement of account which shows all payments, the current balance, etc.
I would also talk to your bank about obtaining proof of payments so that you can prove that the debt was paid. You may have to pay for your bank to get you the records, but there's not much you can do about that. If those records help you prove that you paid the debt in question, then it will be money well spent.
I would then send the records which shows that the debts were paid to the new collection agency. Hopefully that will be enough to get them off your back. You can also send them a cease and desist
letter which tells them not the contact you again. If they attempt to collect again, then they will be in violation of the Fair Debt Collections Practices Act (FDCPA), and you would be entitled to money damages. However, the collection agency would still have the option to sue you. If it sues, then you'll need to produce the bank records (and any other evidence) which proves that the debt was paid. You may then be entitled to money damages under the FDCPA due to the collection agency suing on a bad debt. Fortunately, if you have a claim under the FDCPA, then you would be entitled to attorney's fees, so you would not have to pay for the attorney yourself. Thus, it would be a good idea to contact an attorney in that situation.
Does that answer your question? Let me know if you need clarification, and please remember to rate me positively so that I receive credit for my efforts.
Thank you and good luck!