A Study of JNJ-101556143 With Best Supportive Care in Participants With Metastatic Prostate Cancer

Inclusion Criteria:

* Have histologically confirmed adenocarcinoma of the prostate. Primary (or pathologic evidence of conversion to) small cell carcinoma, carcinoid tumor, mixed neuroendocrine carcinoma, large cell neuroendocrine carcinoma, or sarcoma of the prostate is disallowed
* Progressive metastatic androgen pathway modulation-resistant prostate cancer (mAPMR) defined as having a Prostate-Specific Antigen (PSA) level greater than or equal (\>=) 10 nanograms per milliliter (ng/mL) and at least one of the following: (a) PSA progression defined as at least 2 consecutive increases in PSA value over a previous reference value measured at least 1 week apart. (b) Progressive disease or new lesion(s) in the lymph nodes, bones, or viscera on conventional imaging (computed tomography \[CT\]/magnetic resonance imaging \[MRI\]) as defined by response evaluation criteria in solid tumors version 1.1 (RECIST v1.1) and/or on bone scan per Prostate Cancer Working Group 4 (PCWG4) while on Androgen Deprivation Therapy (ADT) (either surgically \[bilateral orchiectomy\] or with medication)
* Participants should have had all life-prolonging therapies for which they are clinically eligible in the opinion of the investigator and to which they have access
* Prior bilateral orchiectomy or medical castration (receiving ongoing ADT with a Gonadotropin-Releasing Hormone (GnRH) analog \[agonist or antagonist\]) with castrate level of serum testosterone (less than \[\<\] 50 nanograms per deciliter \[ng/dL\] or 1.7 nanomoles per liter \[nmol/L\]) prior to the first dose of trial intervention and must continue this therapy throughout the treatment phase
* Have discontinued concurrent use of any non-investigational systemic anticancer therapy (that is, cytotoxic chemotherapy, Androgen Receptor Pathway Inhibitor (ARPI), radiation therapy) non-sponsor investigational drugs within 2 weeks or Lutetium-177 Prostate-Specific Membrane Antigen-617 (177\^Lu PSMA-617) within 4 weeks prior to randomization and may not have participated in an investigational trial within the sponsor's development program within 6 months prior to randomization
* Toxicity related to prior anticancer treatment that is deemed clinically relevant must have resolved to common terminology criteria for adverse events (CTCAE) Version 6.0 Grade 1 or better

Exclusion Criteria:

* Acute or chronic uncontrolled renal disease, pancreatitis, or liver disease (with exception of patients with Gilbert's Syndrome, asymptomatic gallstones, liver metastases, or stable chronic liver disease per investigator assessment)
* Suspected or known allergies, hypersensitivity, or intolerance to JNJ-101556143 or its excipients
* Had major surgery or had significant traumatic injury less than or equal to 28 days of the first dose of trial intervention
* Spinal cord compression unless considered to have received definitive treatment for this and evidence of clinically stable disease for 28 days
* Solid organ or bone marrow transplantation