What can I do to go back to the US after being deported?

If your only connection to the US is your child, chances of your return to this country is very slim, at least until the child is 21 years and assuming you maintain documented contact in the child's life. Not wanting to wait for your child's 21st birthday, if you try another avenue such as marriage to another US citizen or even certain employment based petitions, whether that will help depends on the reasons why you were deported. You stated that your ex-wife filed a petition for you, but we are unsure if you ever got a green card or if you had a child while your case was before the immigration judge. This is because, if you had a green card and your child was born, with a competent immigration attorney, it should have been helpful in saving you from deportation. Without knowing more about your case, if those factors did not help, this may be saying something about the seriousness of your immigration violations. All immigration charges are not the same and DHS considers some violations so serious that your chances of setting foot in the US again almost impossible even if you are beneficiary of a new current petition. Only a full and detailed consultation with an experienced immigration lawyer who has all the facts of your case can say what your situation is. With that said, I caution you to resist the temptation of illegal reentry to the US due to the severity of the additional criminal and immigration penalties that may await you if you do so without the permission of DHS.

It would help to know why you were deported. The order of deportation can be reviewed by an immigration attorney, who can advise you of your options.