What is a credible witness notary or credible witness notarization? 

There is no such thing as a credible witness notary.  Credible Witnesses are individuals who are willing to swear to the identity of another individual who is signing a document in the presence of a notary public.  The notary who is notarizing a signature may not act as a credible identifying witness.  However, some states allow a notary to identify a signer based on personal knowledge which is similar in nature (but not terminology) to being a Credible Witness.
 
There is also no such thing as a credible witness notarization.  However, you could refer to a notarization as one that uses credible witnesses.  Credible identifying witnesses should not be used unless a proper identification document is not available.  Please also keep in mind that many credible witnesses these days do not know the full name of whomever’s identity they are swearing to.  For the sake of integrity, you might want to ask the proposed credible witness, “What is this man’s full name?”. If they say, “Joe?”, and then shrug their shoulders, then perhaps they don’t know Joe as well as they should to be a credible identifying witness.

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Oath of two credible witnesses
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Subscribing witnesses and Signature by X
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