1. Paytm has dedicated hiring pages in website: Opportunities and Global Recruitment Program
You can keep checking these pages time to time. However, at the time of writing I can not see any open internship open positions.
2. Connect with Facebook: Paytm is connected to facebook via URL https://facebook.com/paytm Like the page and keep in your favorite. Often recruiters love give shoutout on social media while hiring.
3. Twitter is another resource. You can follow Paytm on https://twitter.com/paytm
4. You can register with Jobboards and subscribe for Keyword Paytm. If company will higher through a job board you are registered with, you will get instant alert in your email box.
5. Also you can check on websites like http://www.letsintern.com/ https://internshala.com/ for Internship options with Paytm
Paytm has offices in NCR, Bangalore, Chennai, Mumbai, Kolkata and Toranto
6. You can use social media to Paytm Customer service and ask for email of human resource department. Next you can shoot your resume for Internship positions.