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

The purpose of this study is to evaluate how well JNJ-101556143 works in participants with metastatic androgen pathway modulation-resistant prostate cancer (mAPMR), an advanced form of prostate cancer that has spread and no longer responds to hormone therapy. The study will measure the overall response (tumor shrinkage or disappearance) following treatment with JNJ-101556143.

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). Local-regional disease including invasive disease of rectum, bladder, pelvis is allowed as long as participant has a current or past history of distant metastasis (M1 disease). Participants in Part 1 must have measurable disease per RECIST v1.1 by conventional imaging with CT or MRI (chest, abdomen, and pelvis) and/or Technetium-99\^m (99\^mTc) bone scan confirmed by Blinded Independent Central Review (BICR) at the time of screening * 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 \[\