The purpose of this clinical trial is to learn about the safety, extent of the side effects, and immune responses of the study vaccine (called variant-adapted BNT162b2 RNA-based vaccine) in healthy children. The trial is divided into 5 individual studies or substudies based on age group and prior history of COVID-19 vaccinations. All participants in each of the 5 sub-studies will receive study vaccine as a shot depending on what group they are in. * Substudy A design: Phase 1 includes participants 6 months through less than 4 years 3 months of age who have not received a previous coronavirus vaccination (COVID-19 vaccine naïve) and will receive 3 doses of study vaccine as their initial series, followed by a fourth dose of study vaccine. Phase 2/3 includes participants 6 months through less than 5 years of age who have not received a previous coronavirus vaccination (COVID-19 vaccine naive) and will receive 1, 2, or 3 doses of study vaccine, depending on what group they are in. * Substudy B design: includes participants 6 months through less than 5 years of age who have either received 2 or 3 prior doses of BNT162b2 and will receive study vaccine as their third or fourth dose. * Substudy C design: Phase 1 includes participants 6 months through less than 5 years of age who have received 3 prior doses of BNT162b2 and will receive study vaccine as their fourth dose. * Substudy D design: includes participants 5 through less than12 years of age who have received 2 or 3 prior doses of BNT162b2 and will receive study vaccine as their third or fourth dose. * Substudy E design: includes participants 5 through less than 12 years of age who have not received a previous coronavirus vaccination (COVID-19 vaccine naive) and will receive a single dose of study vaccine.