The disposition of the case hinges on the facts of the case (i.e. what evidence the State claims to have, actual weihgt of the drug, etc...). Your father needs to get an attorney involved immediately. An attorney who not only knows criminal law, but understands and knows immigration consequences as well (or can work with someone who does). Too many times individuals accept responsibility without knowing their acceptance just got them deported.
The attorney your dad has presumably knows the circumstances of his case, and. O one here does. The State could have a great, airtight case against him, like he got caught in a sting operation where he was video and audio taped selling an ounce of cocaine to an undercover officer with a spotless record, and was immediately arrested, so theres no auestion about identity, or there could be all kinds of potential weaknesses with the case that we would have no way of knowing about. What his chances of a dismissal are will depend largely on the strength of the case. If he's here illegally, I would tend to say that his chances of receiving deferred adjudication and avoiding deportation are probably not good--for the specifics of that, you need to talk to his attorney. Good luck--I hope things work out.