Hello,
Don't worry, your admit card would be given to you.
However you are advised to report this problem to the principal of your school as soon as possible. He will tell you further action you need to take or he might rectify the mistake himself.
Aadhad card is generally taken as a identity proof, to match your name etc. However your date of birth might also be matched and it may cause problems, so its better to reach out to your principal.

Good luck