I wasn't deported but left without signing for a waiver as I overstayed with my British passport how can i reenter the US my child is a US citizen

You would probably be best off applying for a visiting visa with the American consulate or embassy rather than attempting to reenter the country on the basis of your British passport. At the consulate or embassy, you could attempt to explain the circumstances of your past entry, and it will then be up to the consular officer as to whether he or she wishes to issue you the appropriate visa. Due to the limitations of the Lawyers.com Forums, Alan Lee, Esq.'s (the "Firm") participation in responding to questions posted herein does not constitute legal advice, nor legal representation of the person or entity posting a question. No Attorney/Client relationship is or shall be construed to be created hereby. The information provided herein by the Firm is general, and requires that the poster obtain specific legal advice from an attorney. The poster shall not rely upon the information provided herein as legal advice nor as the basis for making any decisions of legal consequence.