Can I petition him so that we don’t have to wait three more years before he could apply for citizenship?

Depends on how long he was out of the country with his green card.

He is going to lose his green card status if he is not in the US for the requisite period of time. You cannot petition for him because he is already a green card holder. If he does not lose his status, once he has satisfied the conditions for applying for US citizenship, he will be able to do that on his own.

Your question is confusing. If your son is already a green card holder, then there is no need to petition him, unless he lost his green card through abandonment for staying out of the country for too long. If you are talking about him obtaining his citizenship, there is no petition that you can file for him to get his citizenship sooner. He must wait 5 years from the date he received his green card before applying for citizenship and must have been actually in the U.S. for more than 2-1/2 years of those 5 years. I suggest that you contact an experienced immigration attorney for a face-to-face consultation and give him/her all of the facts surrounding your son's situation. He/she would then be in a better position to analyze his case and advise you of his options.

If your son is already a greencard holder, he needs to be sure to maintain his status and won't be eligible for US citizenship until the time period and sufficient physical presence has past.

Your son will have to meet the citizenship requirements for a green card holder. You cannot help him with this.

No, your son must accrue 5 years of continuous residence as a permanent resident before he qualifies for citizenship. Your citizenship does not make a difference.