Although my father and maternal grandfather are both deceased they were Permanent Resident and Citizen respectively. Can I apply for residency or work

You may or may not be able to apply for residency or work on the basis of your deceased father and paternal grandfather who were permanent resident and citizen respectively. There is no mechanism for a deceased permanent resident father to benefit a child unless the father petitioned for the child prior to passing away. If he had, there are a set of narrow rules under which a child may or may not qualify for benefits. But with respect to your maternal grandfather, he could not transmit U.S. citizenship or any other benefit to you unless he first transmitted such citizenship to your father and your father satisfied a period of physical residence in the States prior to your birth. 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.