You cannot be covered as a dependent under your parents' marketplace plan and apply your tax credit to their premium if your parents do not claim you as a tax dependent. This is because the federally facilitated marketplaces do not currently allow multiple tax households, in this case, you and your parents, to enroll in a plan together and apply any combined tax credits to the premium. Instead, your parents and you must file a separate application for each tax household. Each tax household will be its own policy, although you can pick the same health plan if you choose to do so. If you apply for coverage on your own application, you may qualify for premium tax credits depending on your income.
In general, you can be covered as a dependent up to age 26 on your parent's marketplace policy, but this only happens if your parents claim you as a tax dependent and together, as a tax household, you qualify for financial assistance. (45 C.F.R. § 147.120; 26 U.S.C. § 36B; CMS, Application Spotlight: Family and Household Composition Section, November 2020).