Dear Student,
Anywhere you may apply for studies or job or attaining any type of license you'll be asked for aadhar card as for age proof but you can also give your birth certificate as your age proof as it'll not be a problem. But I might suggest you to get get your aadhar card details corrected to prevent any future loss or charge for misleading personal details or in worst scenario legal charges as it varies from that of your 10th and 12th marksheet. I might suggest you to visit your Nearest Aadhar Center or Aadhar Seva Kendrya and your aadhar corrected.
Hope this might help you.