Inclusion Criteria:
* Male or female children and adolescents aged 3 to \< 30 years, at the time of Screening.
* Patient resides with caregiver who will continue to provide consistent care throughout the study.
* Judged by the Investigator to be in generally good health at Screening based upon the results of medical history, physical exam, 12-lead ECG and clinical laboratory test results. -Laboratory results outside the reference range must be documented as not clinically significant by both the Investigator and Sponsor.
* Participants must have a diagnosis of FXS through molecular documentation of full mutation of the FMR1 gene documented through genetic testing at Screening.
* Patients with a history of seizure disorders must currently be receiving treatment with a stable regimen of no more than two anti-seizure medications (ASMs) for the four weeks preceding study Screening; or must be seizure-free for one year if not currently receiving ASMs.
* Patients taking psychoactive medication(s) should be on a stable regimen of not more than three such medications for at least fours weeks preceding Screening and must maintain that regimen throughout the study. Psychoactive medications include (but are not limited to) antipsychotics, antidepressants, anxiolytics, attention-deficit / hyperactivity disorder (ADHD) medications, and medications for sleep.
* 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 have a body mass index between 12-30 kg/m2 (inclusive) and patients with a body mass index \>30 kg/m2 and \<40 kg/m2 with normal liver function laboratory values and with no immediate family history of fatty liver disease.
* Females of childbearing potential must have a negative serum pregnancy test at the Screening Visit and a negative serum or urine pregnancy test at all designated visits.
* Patients and parents/caregivers must be adequately informed of the nature and risks of the study and given written informed consent prior to Screening.
* Patients and parents/caregivers agree to abide by all study restrictions and comply with all study procedures, and in the Investigator's opinion, 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; females of childbearing potential and male patients with a partner of childbearing potential who are unwilling or unable to use an acceptable method of contraception as outlined below for the duration of therapy and for three months after the last dose of study medication. Standard acceptable methods of contraception include abstinence (defined as refraining from heterosexual intercourse from screening to three months after the last dose of study medication: abstinence only applicable for females \<18 years) or the use of a highly effective method of contraception, including hormonal contraception, diaphragm, cervical cap, vaginal sponge, condom, spermicide, vasectomy, or intrauterine device. The reliability of sexual abstinence needs to be evaluated in relation to the duration of the clinical trial and the preferred and usual lifestyle of the subject. Periodic abstinence (calendar, symptothermal, post-ovulation methods) is not an acceptable method of contraception.
* Patient has transitioned to independent living or living in a residential facility such as a university setting or congregate care.
* History of significant allergic condition, significant drug-related hypersensitivity, or allergic reaction to any compound or chemical class related to ZYN002 or its excipients.
* Exposure to any investigational drug or device less than or equal to 30 days prior to Screening or at any time during the study.
* 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 cannabis or any THC or CBD-containing product within 3 months of Screening Visit or during the study (aside from ZYN002).
* Patient has a positive drug screen, including ethanol, cocaine, THC, barbiturates, amphetamines (unless prescribed), benzodiazepines (except midazolam or comparable administered for blood draws and ECG collection), and opiates.
* Patient is using the following AEDs (medications for the treatment of seizures and/ or epilepsy): clobazam, phenobarbital, ethosuximide, felbamate, carbamazepine, phenytoin, or vigabatrin.
* Patient is using a strong inhibitor/inducer of CYP3A4 or sensitive substrate of CYP3A4 including but not limited to the following medications: midazolam (except single doses administered for the purposes of obtaining blood samples and ECG's), oral ketoconazole, fluconazole, nefazadone, rifampin, alfentanil, alfuzosin, amiodarone, cyclosporine, dasatinib, docetaxol, eplerenone, ergotamine, everolimus, fentanyl, halofantrine, irinotecan, lapatinib, levomethadyl, lumefantrine, nilotinib, pimozide, quinidine, ranolazine, sirolimus, tacrolimus, temsirolimus, toremifene, tretinioin, vincristine, vinorelbine, St. John's Wort, and grapefruit Juice/products.
* Patients may not be taking any benzodiazepines (except single doses administered for the purposes of obtaining blood samples and ECGs) at screening or throughout the study.
* Patient is expected to initiate or change pharmacologic or non-pharmacologic interventions during the course of the study.
* Patient 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 a positive result for the presence of HBsAg, HCV, or HIV antibodies.
* Patient has known history of 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 (TdP) (e.g., heart failure, hypokalemia, family history of Long QT Syndrome), or other serious cardiac problems.
* Any clinically significant condition or abnormal findings at the Screening Visit that would, in the opinion of the Investigator, preclude study participation or interfere with the evaluation of the study medication.
* 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.
* History of treatment for, or evidence of, drug abuse within the past year.
* Previous participation in a ZYN002 study (with the exception of patients who were screen failures in Study ZYN2-CL-016 and did not enter Study ZYN2-CL-017).
* Patient responds "yes" to Question 4 or 5 on the C-SSRS (Children) during Screening or at any time on study.
