Synopsis: India gets involved in the South China sea disputes by drillings and Maritime manovours using the nicobar Islands as its main Naval base. A CPC hawk gets into power and get annoyed and urges India to show constriant, or the consequence will be severe. India is reluctant to act upon the Chinese warning assuming its another complaints from the commies. Chinese general staff then advises the Party secutary to make naval exercises in the nicobar islands. The Chinese fleet consists of 4 Type 054As and 2 052C/D which docks in bay near the indian islands and clashs with a merchant vessel and MOD coast gaurd. This clash eurpts into violence when a Kolkota class DDG intervene and mistakes the dispute between the merchant/Coast guard and the chinesr fleet as an an provocotive action and fires blank shots at the Chinese vessels. The chinese fire a mock AshM but the Indian DDG fires an Bahomas block 2 or 3 missile sinking a Type 054A and damaging another. The Type 052s flees while overhauling the damage vessel. The incident sparks mass protest in China focuing attention from the goverment actions and Japan to India. Hawkish elemants in the PLA high command and the conservative oriented party officals force the Party secutary to send a Carrier tasks force to protect rescure vessels and recive the damaged Type 054A and its remaining personnels. However the objective changed when the Indian navy threatern to block the Malaca straits as part its naval doctrine for incidents like this. Two IN carriers are deployed from the eastern command heads of to the nicobar island base and then closes of the Malaca straits in an attempt of blocking chinese trade. The Indian Carrier Group consist of 5 P-15 or Shilka stealth frigate and 5 Kolkata style DDG with Barak 8 AAM and Bahomas CM. The chinese carrier consists of 4 Type 052A for Medium level AD and 5 Type 052D and 2 Type 055 new 11,000 DDG with 90 H-9/H-18 with long range ABM capability and RW jammers, non radar detective communication with Data link update system and land attack CM with march 2 (lower than bahomas but more smart and sea skimming) and naval version of D-21 Anti carrier/AshM. The IN carrier contains poorer AAD but carriers 40 Mig 29K while China has stronger AAD for its carrier ( Goalkeeper with smart bullets and F-2000 RAAM) and 30 J-15. At the first battle, Indian AWACs discovers a Chineses CBG and alerts the IN CBG blocking malaca to fire fire long range Bahomas. Bahomas travelling March 4 fails to hit the Carrier because the type 052D knocks it out by firing HQ missiles in a rush and damages its VLS modules in a hast to down the Indian missiles. A Indian kilo fires a topedo at the Damaged type 052D and distroys it rudder pralysing it. However a Type 054 detects the sub and fires topedoes at the Kilo and it is distroyed with lose of crew. The 2 Type 55 fires a barrage of DF-21 at the indian Kolkota DDG and Sinks all but one. Knowing it Barak 8 is useless the indians fire every bahomas and sinks the already damaged Type 052DDG and a Type 054A but fails to distroy the PLA CBG. The Carrier of PLA gets close and uses EW warfare against the frigates and lone Kolkota and detects the carrier using OVTL radar and Satallites. Under EW protection a J-15 group task forces gets into air hunts down the IN carrer but fails to sink it as thme face airborne Mig-29K. J-15 trikes the migs into flying the SAM umberella of the medium range missiles of the remaining type 054 and few Migs survive. The superior ASEA of J-15 finish of the last of the migs and gets air dominance. How the Indian carrier retreats with few survivors and China wins.
Considering later comments about DF-21 in which you mention it being specifically meant for US carriers you are clearly referencing the DF-21D correct? That has still not been tested in its intended environment against targets simulating carriers, and so I do not think it should be considered as an operational system in your scenario. Alternatively, it could be included, but then you might as well consider other prototype systems like lasers and hypersonic missiles as operational as well, and change that J-15 task force to a J-20 naval variant task force.
Considering Geographical distance it would seem to me that India would have the logistical advantage, and considering the timeframe China might not be very proficient in carrier group ops (though the only way to be proven is actual combat)
India would also have the advantage in experience with carrier ops as they have operated them longer.
skipping to the effects this would have on the geopolitics in the region IMO...
Overall this sounds like something China would not want to get into as there is little to gain and much to lose. Consider a Chinese win... China has its military capability validated against Indian carriers, and then...? Does it occupy the islands? That would surely face world wide international condemnation considering not only the nebulous nature of the start of the conflict, but accepted sovereign of those islands.
This would very likely turn public opinion in India squarely into the anti-China camp, and lets not begin to talk about how this would affect the government.
Safe to say that I feel the US would find India much more willing to work with it.
What if China didn't occupy the islands? You would still have a less friendly India, one more willing to work against you, and one which now feels it must arm up even further to rectify its loss.
In either case, China very much risks pushing India to take a side, and that won't be China's.
Bottom line:
A conflict between China and India is definitely not in China's best interests.