Will Buying a Domain name changes Adsense earning ?

No. Not directly. But since you do want to earn money out of it, your own domain name is one of the things you'll need to make it look professional. Also, choose universal TLDs like .com, .net and even the newer ones. Don't restrict it with country-specific TLDs. I bought my own domain the second day of creating my blogger site. I've shifted to shared hosting using self-hosted WP a couple of years later and then VPS a couple of years after that, bought a forum software, themes, etc. 

Thanks for replying :-)

If you are already making good income from AdSense, switching to a domain name could result in traffic loss and that could result in loss in AdSense earnings. But since your AdSense is a new one and you are asking this question here, I assume you are quite new to blogging and do not have much traffic currently. So, if you have long term goals in blogging, buy the domain name and start working on good content.

You should have bought a domain name before appying to adsense. Any serious blogger will use their own domain, and even their own host. Consider switching over to self-hosted Wordpress soon. Now, when you are starting out, maybe the best time. 

*This is only a suggestion btw. Many bloggers do well with blogspot.in*

Thanks for suggestions .

If you are redirecting the blogspot to custom domain, then it will affect your earning. Because only some of your visitors will come to your blog via redirection. Means your organic traffic will be lost for sometime. You have to start again means you have to do SEO of your custom domain again. But you will face only a little drop in your earning.