I bought the iPhone 6 gold 64 gb three months ago from USA. But now I'm resident in India. Is there any way to transfer the warranty in India of my phone?
Did you purchase AppleCare? It provides global coverage, so long as the necessary repair is available in the country you are now in. See this page.
If not, the standard Apple Warranty appears to state that if the device is portable, meaning it can operate independently without a power cord, you can obtain warranty service worldwide. (Scroll down on that page to the "Obtaining Warranty Service" section.)