Can we apply to Tata Technologies?

No you can not, recently I was interviewed by Air India and later I was told that you are from tata grp so we can't hire you.

Is there any special requirement, like should complete 2 years like that

Man genuinely, after working at TCS I definitely do not want to work at other companies in the TATA group in IT/software roles.
And yes you can apply for other companies in the TATA group.