Is it possible to patch latest AMI without updating the AMI Id

No, this is not possible.

The binary content of AMIs (meaning the disk content) is inherently immutable. You can't modify it bitwise; any changes require replacing the entire object which would also change the AMI ID. S3 also has built-in mechanisms that consistently verify the integrity of AMIs, across the many copies that are stored in S3.

So once the AMI is created then that content can't be changed: https://docs.aws.amazon.com/AWSEC2/latest/UserGuide/modify-ami.html

A limited set of attributes of an AMI can be changed after it is created - see the API docs for ModifyImageAttribute for details: https://docs.aws.amazon.com/AWSEC2/latest/APIReference/API_ModifyImageAttribute.html