Today we know biological factors of aging like DNA methylation increases & chromosome telomere shortens, that is we have an intrinsic clock. But Einstein suggests time stops at light speed & so should do aging. Question is on which clock, on our watch or body clock? Who has shown DNA methylation stops at high speeds? Why would this happen at all?
If you are traveling near the speed of light relative to another observer, then according to that other observer you are moving through time much slower than he is. But according to you, everything appears normal - your world doesn't become one of slow motion. It's the same for your watch and your body clock. It doesn't depend on the mechanism of time measurement - it's not that moving fast is affecting the gears or circuits in your watch. It's time itself that is slower compared to the other observer.
I think you have a basic misconception here.
Einstein suggests time stops at light speed & so should do aging.
No. This is not what Einstein says and not what time slowing down means.
What time slowing down means is that an observer who sees you traveling at some velocity $v$ sees your time slowing down relative to their own.
However you don't see your own time slow down. Time is completely normal for you. What you see is the observer (who you see moving at velocity $-v$ relative to you) seems to have their time slowed down. Yes, it works both ways !
Both of you see time in your own frame of reference pass normally and the other person's time slow down relative to yours.
Question is on which clock, on our watch or body clock? Who has shown DNA methylation stops at high speeds? Why would this happen at all?
OK, it should be clear that this does not happen at all, but there is another misconception in your question.
It's the "at the speed of light" part.
Objects with a non-zero mass cannot reach the speed of light.
The only things which can reach the speed of light must have zero mass and what's more there is no valid frame of reference for such an object. You cannot describe the passage of time for such an object in the way you would for a massive object. These massless particles always travel at the speed of light and are seen to do so by all observers.