Though the extension of Ayushman coverage to Senior Citizens (70 years and above, not above 60) was announced long ago, the actual registration only started a couple of days ago after inauguration by the PM. My efforts to enroll myself had started earlier than the inauguration and all that I could achieve was registration on the ABHA (Ayushman Bharat Health Account) leading to issuance of an ABHA card and id linked to my Aadhaar, as I was not shown as eligible on the ayushman portal. This was done on abha.abdm.gov.in. ABDM stands for Ayushman Bharat Digital Mission. ABHA is merely a centralised health record for you that can be viewed by healthcare professionals authorised by you.
Later when registering for Ayushman after its inauguration, I found that the registration process asked for two OTPs, one generated by UIDAI for your Aadhaar authentication and the other generated by ABDM for validating your ABHA number. This would seem to suggest that ABHA registration is a prerequisite for Ayushman. However, a search on Google shows that it is not so and ABHA is not a prerequisite for Ayushman. So I suggest that you proceed for Ayushman card directly. If it goes through, you don't have to go through the hassle of creating ABHA account. If it doesn't you can go and complete ABHA registratrion and revert to Ayushman.
In fact in the final step, it gives a checkbox for creating your ABHA account and linking it to your Aadhaar. So you need not go to ABHA creation first.
For Ayushman the process is simple. Go to https://beneficiary.nha.gov.in/ and log in using your mobile number. Alternatively you can download the Ayushman app and use it for this process. The page that opens after login has a button for registration by seniors. Do not input anything in the displayed boxes and directly click that button and complete the form that opens next. In our case who do not belong to the Below Poverty Line group, the family ID has to be left blank.After successful registration you will get a message saying that your card will be ready after some time. You can return the next day and download your card.