You didn't mentioned which exam are you taking about. Now coming to the general view. There may not be any problem during the entry of the examination hall. In most of the examination,the date of birth along with the image of the candidate is matched. But there can be a issue during the admission procedure.

Now rectifying your mistake has a very little possibility.  Once you confirm submission during the application , there you confirm that all the info's you have provided are correct. So in that case they generally doesnt consider another chance for rectification of problems like this.

At this moment , I will say that you should contact the conducting authority of the examination and discuss your problem by a formal mail or a helpline number if provided in the website(Generally every website have one).So you should try to contact and I hope they will give a much proper and officially correct information about what can you do or if there is any considerations that can be made.

Dont get tensed. I wish you all the very best and Good luck so that your problem may get resolved.