Login using AWS cognito with Google auth

Question

I am applying Google Login with CognitoCachingCredentialsProvider and AmazonCognitoIdentityClient but user entry added in the identity pool, not in the user pool. I need to get JWT token for auth. I did research on lots of document but no one gives a proper solution. Please help me with how to achieve social login with AWS Cognito.

           AmazonCognitoIdentityClient cognitoClient = new AmazonCognitoIdentityClient(AWSConnection.AWS_AccessKey,AWSConnection.AWS_SecretKey,AWSConnection.AWSRegion);
        Dictionary<string, string> keyValuePairs = new Dictionary<string, string>() { };
        keyValuePairs.Add("accounts.google.com", idToken);
        GetIdRequest idRequest = new GetIdRequest
        {

            //idRequest.AccountId = _openIdConnect.ClientId;
            IdentityPoolId = "us-west-2:xxxxxx-xxxx-xxxx-xxxx-xxxxxxxxx",

            // set the Dictionary of logins if you are authenticating users
            // through an identity provider
            Logins = keyValuePairs
        };

        // The identity id is in the IdentityId parameter of the response object
        GetIdResponse idResp = await cognitoClient.GetIdAsync(idRequest);

        // TODO: At this point, you should save this identifier so you won’t
        // have to make this call the next time a user connects        
        // create a new request object

        GetOpenIdTokenRequest openIdReq  = new GetOpenIdTokenRequest
        {
            IdentityId = idResp.IdentityId,
            // set the Dictionary of logins if you are authenticating users 
            // through an identity provider
            Logins = keyValuePairs
        };
        GetOpenIdTokenResponse openIdResp = await cognitoClient.GetOpenIdTokenAsync(openIdReq);

I am getting IdToken but I need JWT token for the same. Also, I used this code.

          // Initialize the Amazon Cognito credentials provider
        CognitoAWSCredentials credentials = new CognitoAWSCredentials(
            "us-west-2:xxxxxxx-xxxx-xxx-xxxx-xxxx", // Identity pool ID
            RegionEndpoint.USWest2 // Region
        );
        credentials.AddLogin("accounts.google.com", idToken);
       var sd  = credentials.GetCredentials();

I am getting idToken token from google that is id_token.