why in Skyrim fps below 60 feels too low, like 20-30 in other games? This is very odd
is there any fix?

I understand what you mean, unless my fps is 60 it isn't smooth at all even at 58 fps.

All I have done in the meantime is made sure I have a constant 60fps by choosing the right settings.

Dips from 60fps to say 40fps will feel pretty bad. Unfortunately while mods like SkyBoost improve this, the game is still very much CPU bound, so it's rather difficult to get a constant 60fps without high-end equipment. If you cap your FPS at a lower value however, such as 40fps, then you'll get fluid, constant 40 frames. This will feel absolutely fine, as unless you go below 30, it's not the FPS itself that is jarring, just the dips down to a lower FPS.

Even though I have 60fps everywhere if I cap my fps @ 40 it will jitter and stutter all the time. It doesn't make sense I know but it's like the game doesn't want you to be below 60fps.

What do you use to limit your fps @ 40?

I'm upgrading my GPU in the next few days so I won't need to cap it anymore, but I actually capped at 35fps using a program called Dxtory.

Once you play for a few minutes, you get used to the fluidity and sensitivity and everything seems smooth. I've played the game on the Xbox, and the aiming lag there at 30fps is atrociousness, even just coming from 35fps.

However bear in mind some people are a lot more sensitive to FPS than others. If you're used to playing FPS at 60fps, then getting used to 40fps might be a bit difficult at first. But I just found going from 60-40-35 really jarring because of how different the movement is between different FPS values.

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Perhaps you are getting a micro stutter.

With no description of any hardware involved I can only come to the following conclusion: OP's computer is at fault, you should punish it. I hear they really dislike water.

(That's a joke)