After doing neurosurgery in NIMHANS, do we have the opportunity to go to the U.S.A. & do any fellowships or practice there?

I fail to understand why you are considering fellowship or practice options in the USA when India has highly advanced technologies and is at par with the USA. In fact, Neurosurgery is the one and only super-specialty in India that is known to have state-of-the-art faculties and super-advanced sophisticated instruments that are at par with all developed countries.

India now has almost all subspecialties of neurosurgery that are accredited by MCI. Once you complete your neurosurgery residency at NIMHANS, you will have a plethora of opportunities to do fellowships within India itself. Admission to these fellowship programs is based solely on entrance tests followed by an interview 

These are the most famous fellowships that are accredited by MCI 

• Cerebrovascular & skull base neurosurgery - 1 year
• Spine surgery - 2 years
• Epilepsy and functional base neurosurgery- 2 years
• Pediatric neurosurgery - 1 year
• Neurocritical Care - 1 year
• Once Neurosurgery - 1 year
• Neuro Vascular surgery - 1 year
• Skull base surgery - 1 or 2 year
• Neurovascular intervention - 2 years
• Trauma care - 2 years

Some of the institutes offering these fellowships are AIIMS, NIMHANS, PIGMER, Tata Memorial Hospital - Mumbai, CMC Vellore, etc