Can I File a petition for my son (X) in Africa since I don't have any income and have never work in USA?

has tagged your question as Medicaid and Medicare.  I have relabeled it as an immigration issue so that attorneys experienced in that area can provide you with an appropriate response.

Yes, as the sponsor you will need to file I-864 even if you have no income, showing that you were not required to file taxes with IRS if you had no income. Yes, your other son may be the joint sponsor, or anyone else who can show the requisite income for the household size in question with lawfully obtained income (i.e. in legal status). I would encourage you to have a reputable immigration lawyer assist you in filing the paperwork to sponsor your son. Best regards: GB

Yes, your son "Y" can be a joint sponsor on a 2nd I-864 form ... you still need to file one, even with no income. NOTE: Depending on when you qualify to be a US citizen, it might be faster to naturalize first ... talk to an attorney via Skype.

Yes you can file a petition for your son. As the petitioner you are obligated to file I-864 even though you have no income. You are going to need a joint-sponsor. Your US citizen son can be your joint sponsor.

Yes, you can still sponsor him even without a showing of sufficient income (you will still need to submit Form I864 and comply with supporting evidence). You will need a cosignor to assist who must be a USC or LPR and makes the required amount per immigration guidelines. Consult with an attorney for further guidance. Good luck.