If your father's last entry into the country was legal or if he is eligible for 245(i), you can petition for him on form I-130 and he can concurrently apply for adjustment of status on form I-485. Otherwise, you can petition for him on form I-130 and allow the petition go through consular processing, which will require him to return to his home country to attend his immigrant visa interview at the US consulate. However, the consulate will require him to apply for a waiver on form I-601 after the interview and get it approved by USCIS if he wants to return to the US within 10 years of his departure. He is subject to the 10-year bar because he has presumedly been unlawfully present in the US for 1 year or more. To be eligible for a waiver, he must establish extreme hardship to a spouse or parent(s) who are citizens or permanent residents of the US. He cannot apply for a waiver on the basis of extreme hardship to a child(ren). This matter is very complex and you should seek the advice of an attorney before beginning the process.
Answered on May 15th, 2014 at 3:36 PM