How to add a signature field and verify it?

Hello,

is there a way to add a signature field? 

Once a customer signs, is there a certificate or audit report that can verify the signature? 

Please check this guide to understand how you can add a signature field into your form: How-to-Add-an-E-Signature-to-Your-Form.

A signature field itself is a verification step. Could you let us know the reason why you want to verify a signature and the purpose behind it?

You can check if Adobe E-Sign widget will suit your requirement.