Complaint sub-issue: Information belongs to someone else

In XX/XX/2020 I was alerted by XXXX XXXX that a new account had been opened from XXXX-retail ( XXXX XXXX ) in my name. upon checking I found that it was a card that my wife had taken out for herself for XXXX. The card was in her name and an " aka '' was added to my credit report with my wife 's name. While reviewing the issue we found that they had used my wife 's name, but my SSN ( actually a variation of ) to issue credit. When I tried calling the company at first they could not find an account because the SSN they used does not match mine or my wifes SSN. We found out later that the SSN used was 1 number off of my SSN. When I explained that I did not apply for any credit with them my wife did, they said to send a copy of mine and my wifes license and SS cards so that they could rectify. After I sent in the info, my wife was told to not make payments yet as the account was under review. I sent this information 5 separate times because they kept saying they did not receive the fax. ( even though I have all of the copies saved showing they went through successfully. ) I then received another alert from XXXX XXXX that I had a late payment, sure enough when I checked it was this card, even though they told us just wait on paying until it was fixed they hit by credit anyway. Then after speaking with them they said they did not need my info only my wifes, so fax it again but this time with only my wifes info because sending mine with it was confusing them. So I sent just hers 3 more times. Finally in late XXXX when my wife called them back to make sure they received the most recent fax and she was told yes they received it, and that everything would be handled by that Friday ( 3 days from when she spoke with them ). 2 weeks later I receive another XXXX XXXX update stating that my credit had once again been dinged for nonpayment. I called them back, and this time was told that just because it had my wifes name on it did not mean anything. It was still under my ssn so I was responsible. The account manager told me that it was still not under my SSN it was 1 digit off, so what that tells her is that someone at their office messed it all up, and keyed it in wrong. When I explained again that I did not apply, my wife did with her information, she told me that what I was saying was not true and that my wife stole my info and used it. She then told me that they were canceling the current account and my wife would have to reapply, but that they would still not remove it from my Credit history even though they had the wrong ssn and my wife was telling them that this was her account, and she used her info to get it. She then told me fine, I will put it as fraud and you can try to get them to remove it that way. But we will send a fraud package out and you will have to handle it that way. The worst part is, my wife planned on paying this off the month after she used it. This account would have been paid in full back in XXXX, but they have told us to not make payments until they clear it up. Now I have several credit issues and my score has dropped over 100 points because of this. I am now not able to get the loans I need to refi my home, or even change cellphone carriers because ours does not work well at our new home. I have not had a single late payment on any bill in over 7 years. I worked very hard to make sure nothing ever touched my credit, and this company is now blatantly attempting to ruin my credit over a card that was never mine in the first place. We would pay this card completely off if the company would just fix the issue that they caused in the first place. If they move it to my wifes name and SSN and delete all history from the credit report from me. We do not think it is too much to ask for them to just rectify the issue that they caused. Instead of accusing my wife of theft and calling me a liar. I would be more than happy to give any other information needed. All faxes that I have sent them have been through a secure email fax through my companies email client, and I can show every time I sent it, along with the receipt showing that it was received. I am attaching the letter that my wife received from the company stating that SHE was approved for the card as evidence. Thank you in advance for any help that you can give us during this trying time. 
Account number is XXXX and shows up as XXXX-retail on my credit report.