Inclusion Criteria:  Histology: Metastatic CRPC (mCRPC) with histologic confirmation of adenocarcinoma. Metastatic CRPC with neuroendocrine features or mixed histology is excluded Prior Therapy: Prior treatment with at least 1 prior novel androgen receptor AR-targeted therapy (that is, abiraterone acetate, apalutamide, enzalutamide, darolutamide), or at least 1 prior chemotherapy (example, docetaxel) Eastern Cooperative Oncology Group (ECOG) Performance Status grade of 0 or 1 Measurable disease by Response Evaluation Criteria in Solid Tumors (RECIST) v1.1 or detectable prostate-specific antigen (PSA) levels based on local laboratory results Fertile participants must use a condom with spermicide during any sexual contact with a woman of childbearing potential, including pregnant women, from the time of signing the ICF until 1 year after receiving a JNJ-75229414 infusion. Vasectomized participants must agree to use a condom to protect any sexual partner from exposure to semen for 1 year after receiving the last dose of study drug. Contraceptive (birth control) use should be consistent with local regulations regarding the acceptable methods of contraception for those participating in clinical studies  Exclusion Criteria:  Prior Grade 4 Cytokine release syndrome (CRS) or Grade 3 or Grade 4 neurotoxicity related to any T cell redirection (Bispecific cluster of differentiation [CD 3]) Prior Kallikrein 2 (KLK2)-targeted therapy Prior chimeric antigen receptor T cell (CAR-T) therapy Receiving systemic treatment less than or equal to (<=) 6 months prior to signing informed consent) for any invasive malignancy other than prostate cancer unless approved by the sponsor. Bisphosphonates initiated greater than or equal to (>=) 6 weeks prior signing informed consent are allowed Less than 2 weeks between last administration anti-androgen agents (example, abiraterone or enzalutamide) or radiotherapy, and less than 3 weeks between last administration of cytotoxic chemotherapy (example, docetaxel) or an investigational agent, and apheresis