He can sponsor you under the family-based 3rd preference category as a married son. Unless you are eligible to adjust your status under section 245i (see below), you will eventually have to apply for a green card at the US Embassy in your home country. You will need to demonstrate that your father would suffer "extreme hardship" if you were not permitted to return to the US for ten years.
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(213) 394-4554 x0 Mr. Shusterman is a former INS Trial Attorney (1976-82) with over 35 years of immigration experience. His response to your question is general in nature, as not all the facts are known to him. You should retain an attorney experienced in immigration law to review all the facts in your case in order to receive advice specific to your case. Mr. Shusterman's statement above does not create an attorney/client relationship.
He can petition you, but you face a wait of over 10 years before you can get the green card or even a work permit. Whether you actually can get the green card will depend on what the law is then, due to you overstay.
J Charles Ferrari Eng & Nishimura 213.622.2255 The statement above is general in nature and does not constitute legal advice, as not all the facts are known. You should retain an attorney to review all the facts specific to your case in order to receive advise specific to your case. The statement above does not create an attorney/client relationship. Answers on Avvo can only be general ones, as specific answers would require knowledge of all the facts. As such, they may or may not apply to the question.