Do I need to pursue B.Tech in CSE in an AICTE approved college in order to get government jobs?

Yes you should have your degree from AICTE approved institutions.......but JIIT Noida is a Deemed University and has the right to give degrees under UGC

Yes, you have Your B.Tech is from AICTE Recognised institutes. following is the list of affiliated institute of AICTE http://goo.gl/ojNlLz

For Government job you require a graduation degree from a recognised universty. JIIT, Noida is a Deemed to be University under Section 3 of UGC Act 1956 from 2004. I am of the opinion that non AICTE approval of JIIT will not be any handicap for Government job. You are advised to meet registrar of JI