Enter the below link 

https://appsgate.iitm.ac.in/

Enter your enrollment id and Click on Forgot Registration ID

it will go to the page asking 

https://appsgate.iitm.ac.in/forgotCredentials.html

Forgot your credentials 

Click on Request a OTP

Enter your mobile number and Email ID to reset the new password . 

When you register for gate 2019, you must have given your personal mobile number because most of the communication is done through email or SMS on phone. Open the login window of GOAPS (Gate online application processing system). Click on Login on the right side top of the GOAPS homepage. Since you have the enrollment id, you can enter that and password and click on "Submit". A message will be sent to your registered mobile number.