[Lena]

I am an Indian Cardiothoracic surgeon, wanted to know whether integrated cardiothoracic or fast track residencies will be given to IMGs. Yet to give USMLE have Indian MD in General surgery and Cardiothoracic surgery. Can I get cardiothoracic residency or should I do General surgery and then a fellowship, does my surgical training have any significance during interview?

Exactly what StepTaker said! There are no fast track residencies, its a Gen surg residency and then 3 yrs for a cardio thoracic fellowship. As an old IMG to even get a prelim surgery IV, you'll meed not just high Step scores but US surgery LORs and contacts in programs.
Your Indian experience wont have much of an advantage, plus you'll also need a visa. You are better off trying to get a research fellowship and use it to get into the system. Still not a guarantee, but at least it will help you establish contacts.