Before admission in PhD, please check whether the University (Central, State, Private or Deemed) is appproved by the University Grants Commission (UGC), or not. For this purpose, it is not sufficient to check the website/prospectus of the University, you are required to check the website of UGC (www.ugc.ac.in).
Some countries (especially the Gulf countries) accept Indian degrees. So, if you complete your PhD from a UGC-recognised University (it is immaterial whether it is Private or Deemed), generally it would be accepted in Gulf countries. However, for definite information regarding acceptability of the degree, you have to check with the Department of Education of that particular country (where you are planning to work).
Beware! I question everything and everybody.