Thanks everyone for posting very valuable information. I like to resolve this issue once and for all, and so, I decided to look into the cardpeek data of the EMV chips in my credit cards. I purchased the following card reader from Amazon (worked in Windows 10 laptop) and used the following wiki page to decode my EMVs. EMV data of my credit cards are after the links.
https://www.spotterswiki.com/emv/cardpeek.html
Barclay's AA Aviator Silver Master Card:
CVM 1: Online PIN - ATM cash
CVM 2: Signature - if supported
CVM 3: Online PIN - if supported
CVM 4: Enciphered Offline PIN (ICC) - if supported
CVM 5: Plain Text Offline PIN (ICC) - if supported
CVM 6: No CVM - Always
Comment (1): There are 2 sets of identical CVM lists/files in the card. Why???
Comment (2): This is the most comprehensive CVM among my cards. Barclay's card support both online and offline PIN. Offline PIN (ICC) is supported in both encrypted and plain text modes. So the transaction will be authorized even when the self-service terminal cannot handle encryption. Signature has higher priority (US convention). So PIN will not be asked in the attended terminals.
Comment (3): This is why my Barclay's PIN always worked throughout the world without any issue. Now I am not sure if it is a good idea to cancel the card. Is it enough to justify the $195 annual fee?
Citibank AA Executive Master Card:
CVM 1: Online PIN - ATM cash
CVM 2: Signature - if supported
CVM 3: No CVM - if supported
CVM 4: Online PIN - if supported
Comment (1): Online PIN supported. No offline PIN. tmiw is correct in his/her post.
Citibank AA Platinum Master Card:
CVM 1: Online PIN - ATM cash
CVM 2: Signature - if supported
CVM 3: No CVM - if supported
CVM 4: Online PIN - if supported
Comment (1): Online PIN supported. No offline PIN. tmiw is correct in his/her post.
Comment (2): CVM list is identical to the Excutive card.
Chase Amazon Prime Visa Card:
CVM 1: Online PIN - ATM cash
CVM 2: Online PIN - Manual cash
CVM 3: Signature - Manual cash
CVM 4: Fail - Purchase with cashback
CVM 5: Signature - Always
CVM 6: No CVM - Always
Comment (1): Neither online nor offline PIN available for purchase.
Comment (2): Chase did not mail me a PIN. I just called and requested a PIN. Don't know if the CVM list will change after activating my PIN.
Comment (3): Seems like Chase is very focused on cash withdrawals. Not so much for purchases. Strange???
Elan Fidelity Rewards Visa Card:
CVM 1: Online PIN - ATM cash
CVM 2: Signature - Manual cash
CVM 3: Fail - Purchase with cashback
CVM 4: Signature - Always
CVM 5: No CVM - Always
Comment (1): Neither online nor offline PIN available for purchase.
Comment (2): CVM list is very similar like Chase. But Elan is the card issuer. Is Elan a subsidiary of Chase?
American Express Hilton Aspire Card:
CVM 1: Online PIN - ATM cash
CVM 2: Signature - if supported
CVM 3: No CVM - if not attended cash and not manual cash and not purchase with cashback
Comment (1): Neither online nor offline PIN available for purchase.
Comment (2): There are 2 sets of identical CVM lists/files in the card. Why???
So here we have the full comprehensive conclusion.
If we need unrestricted Chip-and-PIN functionality (online, offline, with-and-without encryption) then we must carry Barclay's AA Aviator Silver MC. It is possible that other cards issued by Barclay's, such as, their no annual fee cards (for example, Jet Blue), have the same CVM structure and priority, but I cannot verify this assumption. Citibank's AA cards will work if and only if a self-service terminal supports online PIN. Chase Amazon Prime VC does not support PIN transactions at all (unless the CVM list in my card updates after I receive and activate my PIN). Elan/Fidelity VC and AMEX Aspire card also do not support PIN transactions.
Your thought? Thanks everyone.