A Study of Azenosertib (ZN-c3) Versus Investigator's Choice Chemotherapy in Subjects With Platinum-Resistant High-Grade Serous Ovarian, Primary Peritoneal, or Fallopian Tube Cancers Positive for Cyclin E1 Protein Expression

Inclusion Criteria: 1. Female age ≥ 18 years 2. High-grade serous epithelial ovarian, primary peritoneal, or fallopian tube cancer 3. Measurable disease per RECIST Version 1.1 4. Eastern Cooperative Oncology Group (ECOG) performance status score 0-1 5. The subject's tumor tissue must be positive for cyclin E1 protein expression per the Sponsor's clinically validated cyclin E1 IHC investigational, in vitro diagnostic assay 6. Prior Therapy: 1. Subject must have platinum-resistant disease 2. One to 3 prior lines or regimens are allowed (1 to 4 prior lines are permitted, if prior mirvetuximab) 3. Prior bevacizumab treatment is required, if eligible per standard of care 4. Prior PARP inhibitor treatment is required if BRCA 1/2 mutation or HRD, if eligible per standard of care 5. Prior mirvetuximab treatment is required, if eligible per standard of care 7. Adequate hematologic and organ function during the screening period Exclusion Criteria: 1. History of another malignancy in the previous 2 years, unless cured by surgery alone and continuously disease-free. Exceptions include appropriately treated carcinoma in situ of the cervix, nonmelanoma skin carcinoma, Stage 1 uterine cancer, or other malignancies with an expected curative outcome. 2. Subjects with primary platinum-refractory disease. 3. Prior therapy with azenosertib or any other WEE1 inhibitor, ATR inhibitor, CHK1/2 inhibitor, or (PKMYT1) inhibitor for PROC. 4. A serious illness or medical condition(s) including, but not limited to, the following: 1. Clinically or radiographically unstable brain metastases or leptomeningeal disease that requires immediate treatment. Subjects with asymptomatic brain metastases are eligible. 2. Acute kidney injury requiring intervention, or presence of indwelling urinary catheter or percutaneous nephrostomy. 3. Significant gastrointestinal abnormalities, including an inability to take oral medication, requirement for IV alimentation, active peptic ulcer, chronic diarrhea or vomiting considered to be clinically significant in the judgment of the Investigator, or prior surgical procedures affecting absorption. 4. Any evidence of small bowel obstruction as determined by air/fluid levels on computed tomography (CT) scan, recent hospitalization for small bowel obstruction within 3 months before randomization, or recurrent paracentesis or thoracentesis within 6 weeks before randomization. 5. Active, uncontrolled infection. Subjects with an infection receiving treatment (antibiotic, antifungal, or antiviral) must have completed such treatment and the infection must be considered controlled/resolved (and afebrile) by the Investigator for at least 7 days before randomization 6. Myocardial impairment of any cause resulting in heart failure by New York Heart Association criteria (Class II, III or IV). 7. Medical or psychiatric condition or laboratory abnormality that may increase the risk associated with study participation or may interfere with the interpretation of study results 5. Any of the following treatment interventions within the specified time frame before randomization: 1. Hospitalization within 14 days 2. Major surgery within 28 days 3. Any chemotherapy or targeted tumor therapy within 21 days or 5 half-lives (whichever is shorter) 4. Radiation therapy within 21 days 5. Autologous or allogeneic stem cell transplant within 3 months 6. Current use of any other investigational drug therapy \< 28 days or 5 half-lives (whichever is shorter) 6. Inability to discontinue treatment with prescription or nonprescription drugs that are prohibited per protocol. 7. Inability to discontinue consumption of food and herbal supplements that are prohibited per protocol 8. Prior wide-field radiotherapy affecting ≥ 20% of the bone marrow. 9. Unresolved toxicity of Grade \> 1 attributed to any prior therapies (excluding Grade ≤ 2 neuropathy, alopecia, or skin pigmentation). 10. Subjects who are immunocompromised or HIV-positive on highly active anti-retroviral therapy 11. Subjects with known active hepatitis B or hepatitis C infection 12. Individuals who are judged by the Investigator to be unsuitable as study subjects