I have BSNL wifi Modem.I am getting Reliance Broadband Connection.The ethernet from reliance does not fit into the
BSNL Wifi Modem.

1)Do we have any type of "adapter" which acts as the intermediate between relaiance wire and my BSNL wifi modem?

Or

2) Do I have to buy a new Netgear wifi router newly?(I checked that the ethernet from reliance fits into netgear router)

There should be a connector for CAT5 or RJ45 on both if not check monoprice.com for your connector. I would consider a newer wireless access point or router if you will get a security or speed boost

If its strictly a wifi modem then it may not(though it should) have an ethernet port at all. And my guess is right now your trying to plug your ethernet into the phone line portion of the modem.