Yes. Alabama Medicaid has several programs for people who also have Medicare coverage: The Qualified Medicare Beneficiary (QMB) program, the Specified Low-Income Medicare Beneficiary (SLMB) program, the Qualifying Individual (QI-1) program, and one for “dual eligibles” with full Medicaid coverage. The services you get depend on how much income you have. These programs pay Medicare premiums, and in some cases, Medicare deductibles and co-insurance. People called “dual eligibles” receive full coverage under both programs.
For details, go to Medicaid's website and click on the “Apply for Medicaid” tab. Click on “Help Paying Medicare Premiums” in the drop down menu, under “Qualifying for Medicaid.”