At the first time, while signup with Gmail and password, firebase saved the credentials correctly. But the next time, I Login with Firebase Google authentication with the same Gmail which i gave while signup, the credentials are overriding in firebase account. After overriding the credentials, we are not able to login using that signup credentials. Can anyone explain how to achieve this?


In the first screenshot you signed in with the email+password provider of Firebase. While this is a valid sign-in method, it means that anyone could've entered that email address, even if they don't actually have access to the Google account for that gmail address.
There is no security risk here, but the level of trust we can put in the value of email address is low. For this reason the emailVerified property of the account is marked as false and you'll typically want to require that the user verify their email address before allowing them to continue.
In the second screenshot, the user signed in with the same email address, but now with the google.com provider of Firebase. This means that Google now verified already that the user has access to the underlying gmail address of the account. Since the google.com provider is the trusted provider for @gmail.com accounts, the system replaces the previous account.
Also see:
You'll typically want to prevent multiple users from signing up with the same email address. For this, you'll want to configure Firebase to only allow a single account per email address in the console, and then use account linking so that the two (email+password and google.com) accounts in your scenario are merged.
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