I need to write a apology letter to the judge for crossing the border illegally

The message you posted does not include a question, but it sounds like you believe that writing a letter to a judge will be important for you to gain immigration-related benefits. Instead of focusing upon writing a letter, it would be wise to engage an immigration attorney whose practice includes a focus on removal/deportation litigation to address the most appropriate steps for you to take under all the circumstances relating to your immigration history, and to represent you in your efforts to be able to live in the United States with your family. David N. Soloway Frazier, Soloway & Kennedy, PC Atlanta, Georgia

I'm not sure where you got the advice to write an apology letter to the Judge but that seems a bit unusual. If the advice to write this letter did not come from an immigration attorney, I would be skeptical of it. I agree with my colleague that instead of groping in the dark - one letter will probably not make a difference, unless part of a good packet of other evidence - you should directly go to an immigration lawyer for the best advice on how to handle this situation.

A letter to the judge by itself will not get you anywhere (unless it puts you into removal proceedings), but a consultation with an immigration attorney might.