As time period doesnot depend on amplitude so then why it is said that in measurement of time period amplitude must be kept small and also that amplitude must be zero ?

If you look at the derivation it includes the line that the restoring force is proportional to # sin theta ~~ theta# (the ‘small angle rule’)

This is less true as #theta# increases.

You did not say what was oscillating. I will answer for the case where it is a simple pendulum that is oscillating. If it is a pendulum, amplitude must be small because the "time period does not depend on amplitude" rule applies to pendulums only if it is exhibiting simple harmonic motion.

Simple harmonic motion of a physical system requires that the force restoring the object (bob) to the equilibrium position must be proportional to the displacement from the equilibrium position.

Go to the site
http://hyperphysics.phy-astr.gsu.edu/hbase/pend.html
Scroll down to the section with a heading of "Period of Simple Pendulum". The first formula in that section is
#F_"net" = m*g*sintheta#,
The angle theta (in radians) is the displacement. This equation comes from valid application of trigonometry.

In that formula, m and g are constants. Therefore this formula says that

#F_"net" " and " sintheta#

are proportional. But the rule for simple harmonic motion says that

#F_"net" " and " theta#

must be proportional. You know that sine is not a linear relation to the angle. It plots a sine wave. But, when the value of #theta# is small, it is a very good approximation to say that

#sintheta = theta#.

When this approximation is valid that initial formula can be written

#F_"net" = m*g*theta#

So in that form, we see that #F_"net" " and " theta# are proportional as required.

So, when amplitude is kept small (allowing use of the #sintheta = theta# approximation), time period is independent of amplitude.

I hope this helps,
Steve

P.S. I do not know why you may have seen "also that amplitude must be zero".