I am a US Citizen, can I petition my father who came over here from Mexico and living in the US?

Yes you can petition for your father to obtain permanent residency - he would be an immediate relative. The only question is 1) whether he can obtain his permanent residency in the U.S. without leaving the U.S. or 2) whether he must process overseas and also obtain a waiver or 3) whether his criminal and/or deportation record would make either strategy too risky. There are various factors that determine the answers to this question: 1) did your father originally come legally and then overstay or did he enter without documentation; 2) did anyone previously petition for your father or for one of his close family members (parent, spouse or child) prior to April 30, 2001; 3) did an employer file for your father or one of his close family members prior to April 30, 2001; 3) was he ever stopped at the border prior to successfully entering the U.S. - if yes, need details; 4) was he ever arrested - if yes, need details; and 5) what facts are there to support an extreme hardship waiver if this is required. If you would like a consultation specifically on his case then contact my office to schedule a consultation and advise fees on the consultation. Once we know the way we have to proceed then we can quote you a specific fee, procedures, and approximate timing.

It depends. We would need to know how he entered the United States.