If you have any such discrepancies then there are no possibilities that you won't be allowed in the examination hall. Although there can be problems during your counselling sessions or admission verification. So I would say you should apply for the correction of your aadhar card and change your DOB. If you don't get the physical copy then also you will have the receipt copy of correction from where you will change the details. Thus if needed you can show that copy in time of counselling.

So its better for you to go to the authorities in order to correct your aadhar. If you don't know where you have to contact to do so then I would recommend you to enquire at your BDO/SDO/Magistrate office. They will provide you the details.

To know more about WBJEE visit the link provided below:

https://engineering.careers360.com/articles/wbjee

I hope this answer helps. All the very best for your future endeavors!