can i apply for health coverage exemption for tax year 2016?

Owe 61K to whom?

There is no requirement to have health insurance on a federal tax return since tax year 2019.

You need legal advice.  Generally speaking, the IRS can't audit you or assess penalties more than 3 years after you file (sometimes, 6 years is allowed).  So generally, they can't be assessing you for 2016-2018 at this point, unless they assessed you a long time ago and you are just now trying to clean it up; or if you never filed for those years (which means the 3 and 6 year clocks never started).  I suspect there are a number of facts you have left out of your question.  You probably need in person help from a tax professional you hire and can work with directly.