Androgen Ablation Therapy With or Without Niraparib After Radiation Therapy for the Treatment of High-Risk Localized or Locally Advanced Prostate Cancer

Inclusion Criteria: * Completion of informed consent prior to any study specific procedures. Consent may be done remotely. * Patients must agree to tissue collection for correlative studies at the specified timepoints * Male aged 18 years and above * Histologically or cytologically confirmed prostate carcinoma * Localized or regional high-risk disease as defined by at least one of the following features: Prostate specific antigen (PSA) \> 20 ng/mL, T3a or higher, grade group 4-5 (i.e. Gleason score ≥ 8) as per National Comprehensive Cancer Network (NCCN) Prostate Cancer Version 2.2020 for high risk or very high risk prostate cancer, and/or regional lymph nodes positive for prostate cancer * Planned for definitive treatment of local regional prostate cancer using XRT and androgen ablation * Willing to undergo ongoing medical castration to maintain testosterone levels of ≤ 50 ng/dL (≤ 2.0 nM) throughout systemic treatment or have undergone bilateral orchiectomy * Eastern Cooperative Oncology Group (ECOG) performance status of ≤ 2. Patients must have adequate organ and bone marrow function measured within 7 days prior to treatment registration as defined below: * Hemoglobin ≥ 10.0 g/dL * Absolute neutrophil count (ANC) ≥ 1.5 x 10\^9/L * White blood cells (WBC) \> 3 x 10\^9/L * No features suggestive of myelodysplastic syndrome (MDS)/acute myeloid leukemia (AML) on peripheral blood smear * Platelet count ≥ 100 x 10\^9/L * Total bilirubin ≤ 1.5 x institutional upper limit of normal (ULN) (except for patients with known Gilbert's disease). (Note: In subjects with Gilbert's syndrome, if total bilirubin is \> 1.5 x ULN, measure direct and indirect bilirubin and if direct bilirubin is ≤ 1.5 x ULN, subject may be eligible.) * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\]) and alanine aminotransferase (ALT) (serum glutamic pyruvic transaminase \[SGPT\]) ≤ 2.5 x institutional upper limit of normal * Calculated creatinine clearance (Cockcroft-Gault Equation) ≥ 30 mL/min * Serum Albumin ≥ 3.0 * Serum potassium ≥ 3.5 mmol/L * Able to swallow study drugs whole as a tablet/capsule * Patients who have partners of childbearing potential (e.g. female that has not been surgically sterilized or who are not amenorrheic for ≥ 12 months) must be willing to use two methods of birth control including adequate barrier protection during the study and for 4 months after last dose of niraparib, abiraterone acetate, and/or apalutamide administration. In addition men should not donate sperm during this period. Please note that the efficacy of hormonal contraception may be decreased if administered with niraparib, abiraterone acetate, and/or apalutamide * Patient is willing and able to comply with the protocol for the duration of the study including undergoing treatment and scheduled visits and examinations including follow up * Medications known to lower the seizure threshold must be discontinued or substituted at least 4 weeks prior to study entry Exclusion Criteria: * Any prior systemic treatment for prostate cancer with the exception of ADT started within 6 months of trial enrollment. Any prior PARP inhibitor therapy * Patients who have prostate cancer with distant metastatic disease * Patients who have had prior major surgery (prostatectomy) or radiotherapy for the treatment of prostate cancer * Any unresolved toxicity (Common Terminology Criteria for Adverse Events \[CTCAE\] grade ≥ 2) from previous anti-cancer therapies * History or current diagnosis of MDS/AML, and/or history of any malignancy \[other than the one treated in this study\] which has a ≥ 30% probability of recurrence within 24 months (except for adequately treated non-melanoma skin cancer, curatively treated in-situ cancer of the cervix or Ta urothelial carcinomas) * Active uncontrolled infection (patients completing a course of antibiotic or antiviral therapy whose infection is deemed to be controlled may be allowed on study after discussion with the principal investigator \[PI\]; the PI will serve as the final arbiter regarding eligibility) * Active or symptomatic viral hepatitis or chronic liver disease * Active pneumonitis or extensive bilateral lung disease of non-malignant etiology * Any underlying medical or psychiatric condition, which in the opinion of the Investigator, will make the administration of study drug hazardous or obscure the interpretation of adverse events. Examples include, but are not limited to superior vena cava syndrome, extensive bilateral lung disease on high resolution computed tomography (HRCT) scan, uncontrolled seizures, history of allogeneic organ transplant, history of primary immunodeficiency or any psychiatric disorder that prohibits obtaining informed consent * Patients unable to swallow orally administered medication and patients with gastrointestinal disorders likely to interfere with absorption of study medication * Patients with a known hypersensitivity to niraparib, apalutamide, and/or abiraterone acetate * Prisoners or subjects who are involuntarily incarcerated * Subjects who are compulsorily detained for treatment of either a psychiatric or physical (e.g. infectious disease) illness * Seizure or known condition that may pre-dispose to seizure (e.g. prior stroke within 1year to randomization, brain arteriovenous malformation, Schwannoma, meningioma, or other benign central nervous system \[CNS\] or meningeal disease which may require treatment with surgery or radiation therapy) * Severe or unstable angina, myocardial infarction (within 6 months prior to enrollment), symptomatic congestive heart failure, arterial or venous thromboembolic events (e.g., pulmonary embolism, cerebrovascular accident including transient ischemic attacks), uncontrolled hypertension, or clinically significant ventricular arrhythmias within 6 months prior to randomization * Current evidence of any of the following: * Gastrointestinal disorder affecting absorption * Active uncontrolled infection (e.g., human immunodeficiency virus \[HIV\] or viral hepatitis) * Any chronic medical condition requiring a higher dose of corticosteroid than 10 mg prednisone/prednisolone once daily * Avoid concomitant strong CYP3A4 inducers during abiraterone acetate treatment. If a strong CYP3A4 inducer must be co-administered, increase the abiraterone acetate dosing frequency * Avoid co-administration of abiraterone acetate with CYP2D6 substrates that have a narrow therapeutic index. If an alternative treatment cannot be used, exercise caution and consider a dose reduction of the concomitant CYP2D6 substrate * Baseline moderate and severe hepatic impairment (Child-Pugh class B \& C) * Any condition that in the opinion of the investigator, would preclude participation in this study