Is UGC fellowship is taxable

Tax-exempt, if issued as research fellowship for Ph.D. thesis submission.

If Fellowship from UGC is for further reserch & studies after PHd then is it exempted?

The reason is utmost important for issue of the fellowship. If its given for research work as per list, and also if TDS not deducted for whatever amount paid, implies it is tax-free u/s. 10(16) of IT act.