Date of Birth from
Customer Configuration in back-end. Those fields are showing in registration page but I also want to add those fields in checkout page too where customer enters address information.
You need to create a module for the new field(s). I used this tutorial to add a date of birth field to my shipping step. The tutorial is for adding a custom field to shipping address but the basics are the same.
(One of the files he uses is missing in the tutorial but it is in the 'sample' that he links at the end)
To find out how to save the data i would like to refer you to this article: