You will need to submit an I-601 waiver and demonstrate that your wife would suffer "extreme hardship" if the USCIS fails to grant you permanent residence in the U.S.
Any time you are told that you need to file a waiver, you need to talk to a qualified attorney. There are only a few situations where that is unequivocally true (if you're in removal proceedings; if you have an arrest; if you are being accused of marriage fraud; and perhaps a few others), and this is one of them. The I-601 looks straightforward, but it is not. It's a discretionary form of relief, and it is difficult to prepare the application without having someone who can evaluate your case from an unbiased perspective. If there is an argument to be made that you are not inadmissible (and I'm not sure that there is), it's something that an attorney in your jurisdiction would need to research and argue. Don't try to do this alone. Good luck.