This FAQ from the German Missions in India (i.e., Embassy, Consulates, and Honorary Consuls) says:
Where do I apply for my Schengen visa, at which German Embassy/Consulate, or at which visa centre?
Apply for a Schengen visa at the German Embassy/Consulate in whose jurisdiction your place of residence lies.
The German missions abroad in India have outsourced the application procedure for Schengen visas to their service partner VFS GLOBAL. The service partner runs visa centres in major cities of India and assists you through the entire application procedure, advises you on the completion of the application documents, collects the visa fee, takes care of the acceptance of the application with fingerprinting and the return of the passport after it is processed by the Embassy/Consulate.
The quickest and most convenient way to apply for the Schengen visa is to go to one of the visa acceptance centres of VFS (see Question 13).
Application forms and visa information can be downloaded free of charge from the website of the relevant mission abroad.
Thus, you should apply through VFS Global.