What is the exact time of sun stay in each zodiac every year on sidereal year duration?
A sidereal zodiac is not the same as the IAU constellations but corresponds more closely to them than the Western tropical zodiac does, e.g. the eastern edge of Virgo remains near Spica despite precession.

I assumed equal 30&deg; blocks of ecliptic longitude with the J285.25 equinox as origin (Lahiri ayanamsa).
Your local tradition may differ slightly, but any difference should affect all signs equally and have little effect on Sun residence times.

I computed these statistics for the years 1970-2070 using Skyfield and the DE430 ephemeris:

     mean  stdev   mean
       seconds     days
 1  2667075 ±186  30.8689
 2  2702097 ±174  31.2743
 3  2717490 ±139  31.4524
 4  2708635 ±122  31.3499
 5  2678191 ±139  30.9976
 6  2635085 ±167  30.4987
 7  2591328 ±182  29.9922
 8  2558345 ±168  29.6105
 9  2544241 ±125  29.4472
10  2552351 ±101  29.5411
11  2580755 ±128  29.8698
12  2622569 ±167  30.3538


Gravitational interactions with other planets tend to make any given year slightly longer or shorter than the mean sidereal year of 31558150 seconds.
For the same 100 years as above, I computed a standard deviation of &plusmn;320 seconds in sidereal year length.