Hello my name is ***** ***** I am delighted to answer your questions today. I have 35 years experience as an immigration lawyer.
Yes you can petition your father as an immediate relative of an adult US citizen child.
Once the petition is approved and the case is transferred to the National Visa Center for his immigrant visa processing (he cannot adjust status in the US because he entered unlawfully), he has to file for a provisional waiver before he leaves to go to Mexico for his immigrant visa interview.
By filing for the provisional waiver while he is in the US he does not get stuck waiting for the waiver to be processed in Mexico after his visa is denied because he triggers a 10 year bar when he departs for the interview.
The form for the provisional waiver is the I-601A and he has to prove it would be a hardship to his wife a lawful resident of the US if he cannot return here as a permanent resident or for her to have to leave the US and live in Mexico to be with him. As the primary bread winner for the resident spouse and possibly minor US citizen children, he has a strong case.
You can read more about it at this link
If you are in a city in CO that has a Catholic Charities Immigration law clinic they do many of these cases and do them for little or no cost.
Google them for your city or google other "free immigration law clinics (your city)"
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