I am considering to apply for a Postdoc in History in South Asia.
I take it you mean a postdoc in
South Asian History, not a job that is at a research university in India or Pakistan.
What does the application material usually consist of? Do I need a sample course syllabus or a teaching philosophy? What should be the focus of my cover letter? Should it talk about my future research project?
This is not my field, so I don't know much about it, beyond saying that as with all postdocs (and jobs) you should include in your application what the SC asks for.
What are some of the research institutions in America and Europe that offer lucrative post-doc positions on South Asia? What are the other forums apart from The Chronicle that I must look at for South Asia post-docs?
Are you even in this field? Surely you would know which are the best institutions for your subject. If you haven't found a position to apply for, why are you asking what should be in your application?
Lucrative and
humanities don't usually exist in the same sentence.