This trial will evaluate the efficacy and safety of ZYN002, a clear cannabidiol gel that can be applied to the skin (called transdermal application) twice a day for the treatment of behavioral symptoms of Fragile X Syndrome (FXS). Eligible participants will then participate in up to a 14 week treatment period, where all participants will receive placebo or active study drug. Patients ages 3 to < 18 years, will be eligible to participate.

This is a randomized, double-blind, placebo-controlled, multiple-center study, to assess the efficacy and safety of ZYN002, a pharmaceutically manufactured cannabidiol, formulated as a transdermal gel, for the treatment of children and adolescent with FXS. Approximately 204 male and female patients, ages 3 to < 18 years, will undergo a screening process. Eligible participants will be randomized 1:1 to either trial drug or placebo and will undergo a 14-week treatment period. Randomization will be stratified by gender, weight category and geographic region. All participants may receive placebo during the trial. Participants who are taking anti-seizure drugs may undergo an additional 1-2 weeks of blinded treatment to taper off study drug treatment. The assignment will be done by a computer generated system and neither the trial doctor or the participant or their caregivers will know which treatment is being given to them. The dose of the treatment will depend on the weight of the participants. If the participants weigh less than or equal to 35 kg, they will receive 2 sachets of the gel twice a day (1 sachet approximately every 12 hours) and if they weigh more than 35 kg, they will receive 4 sachets of gel per day (2 sachets approximately every 12 hours). Parents/ caregivers will be instructed on proper application of the gel. The gel will be applied to clean, dry, intact skin of the upper arms/ shoulders.

Blood samples will be collected for safety analysis of ZYN002. An independent analytical laboratory will also perform CGG repeat and methylation status analyses. Additionally, the parents/caregivers will be asked to complete some questionnaires. There will be other questionnaires and scales that will be completed at the site by the trial doctor.

After the final dose, patients will be followed weekly for 4 weeks by telephone, prior to discharge from the study.

Inclusion Criteria:

• Male or female children and adolescents aged 3 to less than 18 years, at the time of Screening.
• Diagnosis of FXS through molecular documentation of FMR1 full mutation.
• Judged to be in good health based on physical exam, 12-lead ECG and clinical laboratory test results.
• Patients must be assessed by the Investigator as being moderately to severely impacted due to FXS.
• Patients taking psychotropic medication(s) should be on a stable regimen of not more than two such medications for at least fours weeks preceding Screening and must maintain that regimen throughout the study.
• If patients are receiving non-pharmacological, behavioral and/or dietary interventions, they must be stable and have been doing so for three months prior to screening.
• Patients and parents/caregivers must be adequately informed of the nature and risks of the study and given written informed consent prior to Screening.
• In the Investigator's opinion, patients and parents/caregivers are reliable and willing and able to comply with all protocol requirements and procedures.

Exclusion Criteria:

• Females who are pregnant, nursing or planning a pregnancy.
• Alanine aminotransferase (ALT), aspartate aminotransferase (AST) or total bilirubin levels greater than or equal to 2 times the upper limit of normal or alkaline phosphatase levels greater than or equal to 3 times the upper limit of normal.
• Use of a strong inhibitor/inducer of CYP3A4 or sensitive substrate of CYP3A4.
• Use of minocycline for 30 days prior to screening or throughout the study.
• Use of any benzodiazepine at screening or throughout the study.
• Use of THC or CBD-containing product within three months of Screening Visit or during the study.
• Change in pharmacologic or non-pharmacologic intervention during the course of the study.
• Any skin disease or condition including eczema, psoriasis, melanoma, acne, contact dermatitis, scarring, imperfections, lesions, tattoos, or discoloration that may affect treatment application, application site assessments or absorption of the trial drug.
• Patient is using the following ASMs: clobazam, phenobarbital, ethosuximide, felbamate or vigabatrin.
• Patients has an advanced, severe or unstable disease that may interfere with the study outcome evaluations.
• Patient has acute or progressive neurological disease, psychosis, schizophrenia or any other psychiatric disorder or severe mental abnormalities (other than FXS) that are likely to require changes in drug therapy or interfere with the study objectives or ability to adhere to protocol requirements.
• Patient has suspected or confirmed cardiovascular disease, advanced arteriosclerosis, structural cardiac abnormality, cardiomyopathy, serious heart rhythm abnormalities, coronary artery disease, cardiac conduction problems, exercise-related cardiac events including syncope and pre-syncope, risk factors for Torsades de pointes (e.g. heart failure, hypokalemia, family history of Long QT Syndrome) or other serious cardiac problems.
• History of treatment for, or evidence of drug abuse within the past year.
• Patient responds "yes" to Question 4 or 5 on the C-SSRS (Children) during Screening or at any time on study.