Unable to upgrade Apache2 to 2.4.48 in Ubuntu 16.04 Server

Manfred Hampl suggests this article as an answer to your question:
FAQ #3037: “no rolling release”.

Ubuntu 16.04 is in ESM (Extended Security Maintenance) mode. This means that there are only security patches available for those who have registered for paid support and no other updates are done any more. A version upgrade for software is not intended in that status.

If you need a newer version of apache2, then you have to switch to a newer Ubuntu release, but please note that apache2 version 2.4.48 is not yet available for any Ubuntu release (but will probably be published with Ubuntu 21.10 later this year).

Eventually you can find such version in a PPA.

The question in comment #3 (now hidden) was:
"Which is the last stable version supported in ubuntu 16.04??"

There is only one supported version for each Ubuntu release and no "last stable version" that is supported.
It usually is the one that was current when the Ubuntu release in question was published. (Did you read the FAQ linked above?)

For Ubuntu 16.04 Xenial Xerus it is 2.4.18-2ubuntu3.17 (which is version 2.4.18 enhanced by some patches to fix vulnerabilities).
see https://launchpad.net/ubuntu/+source/apache2

You may find a PPA here on Launchpad
https://launchpad.net/ubuntu/+ppas?name_filter=apache

I don't suggest you use these in industry in production (CAB would laugh you out, or should).

I suggest a side by side upgrade (if production) and test, once the new server is good, swap the networking under change and the new server will work with no effort needed.

If this is a home server then I suggest you do same (if it is a VM) or simply wipe the old unsupported OS off, do a clean install of Focal (Ubuntu 20.04) then restore your web site data etc from your backups