If either of the biological parent is a citizen of a particular country and are biologically linked to the child; they can lawfully lodge a "Citizenship be descent" application with their respective embassy/ high commission in India itself.
We at Become Parents suggest a paternity DNA test following the birth of your baby to verify and speed up the process with your embassy. Normally the time taken by Australian / British and American Embassies is approx 3-4 weeks at the max.
Please check with your local immigration office to verify this. But we will help you lodge all the paperwork (both medical and legal) to obtain the necessary travel documents. We have a team of specialist family law specialist that will get the court papers and documentation ready to lodge with the embassies and high commissions.
If you have any further questions regarding this please contact us.