A Study to Evaluate the Safety and Immunogenicity of the mRNA COVID-19 Vaccines in Healthy Children Between 6 Months to Less Than 6 Years of Age

Inclusion Criteria: * The participant is 6 months to \<6 years for Parts 1, 2, and 3; 2 years to \<5 years for Part 4A; and 6 months to \<2 years for Part 4B at the time of consent (Screening Visit). Note: for Part 1, participant must be at least 6 months old and must not have reached 6 years of age at the time of administration of first dose. For Part 4B, the participant must be at least 6 months old and must not have reached 2 years of age at the time of administration of first dose. * If the participant has a chronic disease (that is, asthma, diabetes mellitus, cystic fibrosis, human immunodeficiency virus \[HIV\] infection), the disease should be stable, per investigator assessment, so that the participant can be considered eligible for inclusion. Stable diseases are those which have had no change in their status or in the medications required to control them in the 6 months prior to Screening Visit. Note: a change in medication for dose optimization (that is, insulin dose changes, adjustments for age-related weight gain), change within class of medication, or reduction in dose are not considered signs of instability. * In the investigator's opinion, the parent(s)/legally authorized representative(s) (LAR\[s\]) understand and are willing and physically able to comply with protocol-mandated follow-up, including all procedures and provide written informed consent. * The participant is 2 years or older and has a body mass index (BMI) at or above the second percentile according to World Health Organization (WHO) Child Growth Standards at the Screening Visit. OR * The participant is less than 2 years of age and the participant's height and weight are both at or above the second percentile according to WHO Child Growth Standards at the Screening Visit. Special inclusion criteria for participants aged 6 months to \< 12 months: * The participant was born at full-term (≥ 37 weeks gestation) with a minimum birth weight of 2.5 kilograms (kg). Inclusion criteria for Part 2: * The participant must have received 2 doses of mRNA-1273, approximately 28 to 35 days apart, as 25-μg primary series, and second dose was given at least 4 months prior to enrollment. Inclusion criteria for Part 3 only: \- The participant must have received an age-appropriate immunization series of an authorized/approved COVID-19 vaccine, with the last dose given at least 4 months prior to enrolment (Previous vaccines NOT allowed are: XBB.1.5-containing formulation). Exclusion Criteria: * Has a known history of SARS-CoV-2 infection (that is, reported AE of COVID-19 or asymptomatic SARS-CoV-2 infection during Study mRNA-1273-P204 at the time of rollover into mRNA-1273-P306 or during Part 1 at the time of rollover into Part 3) in the 90 days prior to dosing in this study. * Is acutely ill or febrile 24 hours prior to or at the Screening Visit. Fever is defined as a body temperature ≥ 38.0°Celsius (C)/≥ 100.4°Fahrenheit (F). Participants who meet this criterion may have visits rescheduled within the relevant study visit windows. Afebrile participants with minor illnesses can be enrolled at the discretion of the investigator. * For Parts 1 and 4, participant has previously been administered an investigational or approved CoV (that is, SARS-CoV-2, SARS-CoV, Middle East respiratory syndrome coronavirus \[MERS-CoV\]) vaccine. For Part 2, participant who received any approved/investigational CoV vaccine are ineligible to participate except for those who received mRNA-1273 (prototype) vaccine. * Has undergone treatment with investigational or approved agents for prophylaxis against COVID-19 (including receipt of SARS-CoV-2 monoclonal antibodies for prophylaxis or treatment) within 90 days prior to enrollment. * Has a known hypersensitivity to a component of the vaccine or its excipients. Hypersensitivity includes, but is not limited to, anaphylaxis or immediate allergic reaction of any severity to a previous dose of an mRNA COVID-19 vaccine or any of its components (including polyethylene glycol \[PEG\] or immediate allergic reaction of any severity to polysorbate). * Has a medical or psychiatric condition that, according to the investigator's judgment, may pose additional risk as a result of participation, interfere with safety assessments, or interfere with interpretation of results. * Has a history of diagnosis or condition that, in the judgment of the investigator, may affect study endpoint assessment or compromise participant safety, specifically the following: * Congenital or acquired immunodeficiency, other than well-controlled HIV infection. * Chronic hepatitis or suspected active hepatitis * A bleeding disorder that is considered a contraindication to IM injection or phlebotomy * Dermatologic conditions that could affect local solicited AR assessments * Any prior diagnosis of malignancy (excluding nonmelanoma skin cancer) * Has received the following: * Any routine vaccination with inactivated or live vaccine(s) within 14 days prior to study vaccination or plans to receive such a vaccine through 14 days following study vaccination. Note: This excludes influenza vaccine that may be given anytime, but ideally at least 7 days before study dose. If a participant receives an influenza vaccine, this should be captured within the concomitant medication electronic case report form (eCRF). * Systemic immunosuppressants or immune-modifying drugs for \>14 days in total within 6 months prior to the day of enrollment (for corticosteroids, ≥1 milligrams (mg)/kg/day or ≥ 10 mg/day prednisone equivalent, if participant weighs \>10 kg). Participants may have visits rescheduled for enrollment if they no longer meet this criterion within the Screening Visit window. Inhaled, nasal, and topical steroids, and palivizumab are allowed. * Intravenous (IV) or subcutaneous (SC) blood products (red cells, platelets, immunoglobulins) within 3 months prior to enrollment. Note: Other inclusion and exclusion criteria may apply.