Is there anything that I need to set if I am hosting my own supabase to handle a lot of incoming connection? Let's say about 1 million connections to database.

This isn't really a Supabase specific question, this is a general hosting/scaling question. It's best to search for information related to this on Google. Also are you getting 1 million connections to your database at the moment? otherwise this is just premature optimisation for something that isn't currently happening.