National Eligibility Test will be conducted by UGC Only
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University Grants Commission (UGC) will continue to conduct National Eligibility Test (NET).

There is no declaration to entrust the responsibility of holding NET to other body apart from UGC, Ministry of Human Resource Development (MHRD) mentioned in Rajya Sabha on July 21, 2017 as reported by The Times of India.

CBSE has been conducting the UGC-NET exams directed by MHRD. 

There is no consideration of handing over the responsibility of conducting NET exam to any other body or through any other mechanism” stated in a written reply by Upendra Kushwaha, ministry of state, HRD.

The exam is held twice a year first in July and other in December- for the grant of junior research fellowship and eligibility for assistant professorship in colleges and universities.