Legally, you have no contractual relationship with B since B is a subcontractor, who only has privity of contract with the general contractor A. Once you paid A in full you have nothing to worry about and you have no obligation to show anything to B. B could only bring a contract dispute against A.
It sounds like B wants your help to gather evidence in his suit against A. BTW, "sue" means civil and in criminal court we say "prosecute". B cannot bring a criminal charge against A since that is a matter of the state. B could have just asked you for help. His way of discovery is unreasonable. He could subpoena your record but that effort will almost guarantee to fail since you are not a party in the lawsuit.
That being said, there is a way B can force you to show the record by filing a mechanics lien on your property since he did the work and has not been paid and he is in no way verifying the information whether you paid A in full. Once a mechanics lien is filed with the clerk, who has no other information but accepting the filing, you have to show to the clerk the payment record in order to vacate the lien, or be forced to fight in a foreclosure suit with B. So if I were you just give B the record so he could collect his money. A has his own problem to deal with but lying to B would bring him into bigger trouble.
