A Study of JNJ-98768111 in Participants With Advanced Prostate Cancer

The purpose of Part 1 of this study is to find out how safe JNJ-98768111 is and the most suitable dose (recommended phase 2 dose \[RP2D\]) regimen(s) of JNJ-98768111. The purpose of Part 2 of this study is to find out how safe JNJ-98768111 is at the RP2D regimen(s) in participants with advanced prostate cancer (cancer of the prostate, a male reproductive gland found below the bladder, which has spread extensively to other parts of the body).

Inclusion criteria: * a. Histologically confirmed adenocarcinoma of the prostate. Adenocarcinoma with small cell or neuroendocrine features is permitted. b. Measurable or evaluable disease (metastatic prostate cancer) based on computed tomography (CT), magnetic resonance imaging (MRI), or bone scan. Prior treatment with at least 1 prior novel androgen receptor (AR)-targeted therapy. c. Serum prostate-specific antigen (PSA) value greater than or equal to (\>=) 2 nanograms per milliliters (ng/mL). d. Prior orchiectomy or medical castration; or, for participants who have not undergone orchiectomy, must be receiving ongoing androgen deprivation therapy (ADT) with a gonadotropin releasing hormone (GnRH) analog (agonist or antagonist) prior to the first dose of trial drug and must continue this therapy throughout the treatment phase; e. Castrate levels of serum testosterone as defined in the protocol, prior to the first dose of trial intervention; f. Progressive metastatic disease following their most recent line of therapy. Disease progression will be defined by at least one of the following: PSA progression, radiographic progression according to response evaluation criteria in solid tumors (RECIST v1.1), or progressive bone disease according to prostate cancer working group 3 (PCWG3) criteria * Eastern cooperative oncology group (ECOG) performance status of 0 or 1 * Agree to all of the following during the trial and for 6 months after the last dose of trial drug: a. Use a highly effective method of contraception; b. Wear a condom when engaging in any activity that allows for passage of ejaculate to another person; c. Not to donate sperm or freeze for future use for the purpose of reproduction; d. Not plan to father a child. In addition, the participant should be advised of the benefit for a female partner to use a highly effective method of contraception * Sign an informed consent form (ICF) indicating that the participant understands the purpose of, and procedures required for, the trial and is willing to participate in the trial Exclusion criteria: * Active central nervous system (CNS) involvement * Toxicity related to prior anticancer therapy that has not returned to Grade less than or equal to (\