I am age 60 and have been receiving Social Security disability insurance (SSDI) payments for two years. I recently received my Medicare card, and I would like to get coverage to supplement my Medicare Part A and Part B coverage. I live in a state that does not require insurance companies to sell Medigap supplemental policies to people under age 65. Can I purchase a Marketplace plan to supplement Medicare?

No, companies that sell Marketplace plans are prohibited from selling these plans to you if they know you are covered by Medicare.  If you do not live in a state that requires insurance companies to sell Medigap policies to people under age 65, some insurance companies still may voluntarily sell Medigap policies to people under 65, although they will probably cost you more than Medigap policies sold to people age 65 and older.  If you want prescription drug coverage to supplement your Medicare Part A and Part B benefits, you can purchase a Part D prescription drug plan.  You can also look into receiving your Medicare-covered benefits through a Medicare Advantage private plan, such as an HMO or PPO.  Medicare Advantage plans are not allowed to turn down people with Medicare based on your health status or having a pre-existing condition, but access to providers is generally more limited than in traditional Medicare.
Keep in mind that when you turn 65 and are enrolled in Part B, you will get a six-month opportunity to enroll in any Medigap policy you want.