Yes you are right CMC does have provision to offer the graduate or postgraduate or post doctorate seats on sponsorship which is being sponsored by local govt or christian society. To avail the sponsorship one must adhere or fulfill the criteria, please explore the cmc website and get the form downloaded. Application must be reached The registrar, CMC, Vellore, the last date of application is 14th April. Such quota is available for the weaker section of society those come from underprivileged society and having incredible academic record, moreover they need to qualify the two-tier examination system to prove it only then CMC consider the admission.

If CMC Vellore or council member does not consider the sponshorship then one must explore the undergraduate college sponsorship, might be recommended for the admission with full support. Such candidtae does not pay more than Rs five hundred towards the registration fee.
I do not much about your profile whether you fall into sponsorship category or not if so then must read the eligibility criteria and also know who can be the sponsor for your medical study at CMC Vellore:

1. A sponsor may be christian church or christian organization which is a member of christian medical college association
2. Any other body which is facilitating or running medical hospital and having distant membership of the christian medical college association either in india or any neighboring country.

3. The christian medical college vallore is also a recognized sponsor of the medical students.
4. Indian sponsoring body may fund only indian citizen
5. Admission is restricted to only one member of family in a year
6. No sponsored candidate is considered for admission unless clearing the full set of admission test only they can consider for the successful attempt.
6. There is service obligation for two years after passing the medical course, one has to serve any member hospital for two years in a continuation, after the completion of service your transcript will be handed over to you, moreover you can continue the service for longer period as per the normal terms and conditions.
7. If a candidate is not falling into the set criteria then he / she will be considered as open category.

hope above cited information will serve your purpose and i wish good luck to go for such prestigious medical service.