If you have Medicare, you cannot buy a plan in the Marketplace except under limited circumstances. Companies that sell Marketplace plans are prohibited from selling these plans to you if they know you are covered by Medicare. The exception to this rule is when the individual buying coverage has lost high risk pool coverage that they used to supplement Medicare.
However, a small number of individuals are enrolled in Medicare Part A and paying premiums (typically those who have not paid Medicare taxes for 10 years or more). These individuals may be eligible for a premium tax credit if they are not enrolled in Medicare and coverage through a health insurance Marketplace may be the best option for them. (Section 1882(d)(3)(A) of the Social Security Act; IRS, Notice 2013-41).