Latest supported Kernel for Ubuntu 20.04

Latest supported Kernel for Ubuntu 20.04

The officially supported kernels are in the Ubuntu repos.

There are different aspects:

The original version of the kernel for Ubuntu 20.04 was 5.4, and there are still modifications provided to cope for bugs and improvements, e.g. the version from 12 January 2023 includes fixes for the vulnerabilities CVE-2022-3643, CVE-2022-43945, CVE-2022-45934 and CVE-2022-42896

Newer Ubuntu releases are delivered with newer version families of the kernel, and these are also backported to older Ubuntu LTS releases. See https://ubuntu.com/about/release-cycle#ubuntu-kernel-release-cycle
For Ubuntu 20.04 you currently can install hwe kernels in versions 5.8, 5.11, 5.13 and 5.15
At the moment there is no hwe package for the 6.* kernels yet. This depends on the version in the newest Ubuntu release, and Ubuntu 23.04 currently is still on the 5.19 version of the kernels.
If the next Ubuntu release will have a 6.* version kernel, then this will also be made available for older Ubuntu releases like 20.04

The "Canonical Kernel Team" is already working on packages with kernel version 6.1, but I do not know whether the next Ubuntu release (to be published in April) will already contain a 6-* kernel or still an older one.

For your statement "There was some vulnerabilities reported for Kernel below 6.0.x.", please provide more details. I assume that attempts will be made to fix these bugs also in older versions of the kernel (see the CVE numbers above).

If you insist on a 6.* version kernel already now, then you can try installing the mainline version of the kernel yourself, see https://wiki.ubuntu.com/Kernel/MainlineBuilds and https://kernel.ubuntu.com/~kernel-ppa/mainline/?C=N;O=D
Please be aware that you will not get support from Ubuntu when doing that.