have (one) cold
To have one utterly under control, to the extent that their actions can be dictated. Please don't report me to the headmaster. You have me cold! Once the gangsters were able to blackmail Susan, they had her cold.
have someone cold
have someone at your mercy. US informal 1988 Rodney Hall Kisses of the Enemy He waited in his office for news of violence, knowing that then he would have the troublemakers cold.