I am clearly asking about MOSFETs, so gate current should be much smaller than drain current.
Sure, if you were clear, but you were not. Just what is
"cutoff current" supposed to mean to the average person
schooled in the art? Drain current, unless you say otherwise.
You didn't until this #4 post.
Short of breakdown there will be some gate leakage which
the manufacturer only specifies a one-sided (max) limit
for, and quite often only for the "on" condition Vgs(max)
(expecting the user to not overdrive the gate, as this can
pose other problems as well).
There's no answer for MOSFETs generically. Gate oxide
thickness, quality, area and the effects of field control
structures (i.e. how much field the oxide sees, under
operating conditions) all matter. And all of them are device-
design as well as wafer-shot specific.
If you had -a- device in mind the datasheet would give
you some guidance about the corners of the "box".
And for the power MOSFETs which incorporate a gate
protection diode, which are some, all of this goes out
the window.
Now in post #6 you're back to drain current which is what
I told you about originally. Which is certainly dependent on
drain voltage and temperature. All of which you'd look to the
specific product datasheet, to say - not ask people to make
up an untethered guess.