A collection agency keep calling me for an AMEX payment . But I never had any AMEX credit card .?

First of all, your account or not I do not told you that an affidavit removes a collection off your report. The most thats going to do is have all three credit bureaus list you as a Credit Fraud alert, which in my opinion looks worse to creditors. You need to call them and get this resolved before it shows up on the credit bureaus. Ignoring credit issues makes things worse.