Can I get residency, green card, to take care of my father who is 78 years old, retired and with only one hand ? I would like to take care of him.

This is probably a difficult request that you are asking for four reasons. First there is no nonimmigrant visa that would allow you to do this. Second you appear to be an overstay and would be subject to a 10 year bar if you left the United States. Third a green card employment case for doing this requires that you have paid experience in the occupation other than through taking care of your father. Other obstacles to an employment case are that trying to get a green card through employment means that the applicant generally does not have a strong familial relationship with the sponsor, in this case your father; and that the sponsor has to have sufficient financial strength to pay prevailing wages to an applicant. Fourth a deferred action case in which the government withholds removal and gives work authorization is very unlikely in this political atmosphere.  A more viable route, but one that takes much longer, is for your father to sponsor you as his son or daughter. If you are single, the case would take approximately 7-8 years and if you are married approximately 13 years. Your father would file an I-130 relative preference petition for you and upon approval, you would file for an I-601A waiver of the 10 year bar while still here in the US. If both the I-130 petition and the I-601A  are approved, and when the waiting list is almost at an end, you would consular process your case and be interviewed for an immigrant visa at the American consulate or embassy in your home country. Assuming that the interview goes well, you would likely return to the US within 1-2 months with an immigrant visa. Your stepmother could do the same for you if your father married her before you turned 18.  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.