Hey Ritika !
Of course you can apply for the AIIMS MDS form even if you are doing your MBBS from a Pvt. medical College.
The only criteria to be elligible to appear for the examination is

1. You must complete your 12 month mandatory internship so that you can produce the completion certificate on the due date.
2. A minimum aggregate percentage of 55% in your Profs. if UR, and a minimum of 50% if from reserved categories.

You can go through the eligibility criteria through :

https://www.google.com/amp/s/medicine.careers360.com/articles/aiims-pg-eligibility-criteria/amp

Hope this helps.

Best Wishes !

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