• Histologically or cytologically confirmed metastatic or refractory/recurrent HPV-16+ cancer.

• Tumor with HPV16 genotype as determined by testing performed in a CLIA certified laboratory.

• HLA-A\*02:01 allele as determined by testing performed in a Clinical Laboratory Improvement Amendments (CLIA) certified laboratory. Participants may be enrolled based on low resolution typing (i.e., HLA-A\*02) but the HLA-A\*02:01 allele type must be confirmed prior to apheresis.

• Measurable disease as assessed by RECIST Criteria Version 1.1.

• Age ≥ 18 years.

• Eastern Cooperative Oncology Group (ECOG) performance status 0 or 1 at screening.

• Must have received prior first line standard therapy or have declined standard therapy.

• Standard treatment options for first and second-line therapy must be presented and formally declined (Appendix VII).

• Patients with three or fewer brain metastases that have been treated with surgery or stereotactic radiosurgery are eligible. Lesions that have been treated with stereotactic radiosurgery must be clinically stable for one month before protocol treatment. Patients must be fully recovered from surgery.

⁃ Negative pregnancy test for women under 55 and all women who have had a menstrual period in the last 12 months. A pregnancy tests is not required for women who have had a bilateral oophorectomy or hysterectomy.

⁃ Men and women of child-bearing potential must agree to use adequate contraception (i.e., intrauterine device, hormonal barrier method of birth control; abstinence; tubal ligation or vasectomy) prior to study entry and for four months after treatment. Should a women become pregnant or suspect she is pregnant while she is participating in this study, she should inform her treating physician immediately.

⁃ Seronegative for HIV antibody, hepatitis B antigen, and hepatitis C antibody. If a hepatitis C antibody test is positive, then testing for antigen by RT-PCR for Hepatitis C (HCV) RNA must be negative.

⁃ Participants must have organ and marrow function as defined below:

∙ Leukocytes \> 3,000/microliter (mcL)

‣ Absolute neutrophil count \> 1,500/mcL

‣ Platelets \> 100,000/mcL

‣ Hemoglobin \> 9.0 g/dL

‣ Total bilirubin within normal institutional limits except in participants with Gilbert's Syndrome who must have a total bilirubin \< 3.0 mg/dL.

‣ Serum aspartate transferase (AST) (SGOT)/alanine transaminase (ALT) (SGPT) \< 2.5 x upper limit of normal (ULN)

‣ Calculated creatinine clearance (CrCl) \>50 mL/min/1.73 m2for participants with creatinine levels above institutional normal (by the Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) equation).

‣ international normalized ratio (INR) or activated partial thromboplastin time ( aPTT) ≤1.5 X ULN unless the subject is receiving anticoagulant therapy. Subjects on anticoagulant therapy must have a PT or aPTT within therapeutic range and no history of severe hemorrhage.

⁃ More than four weeks must have elapsed since any prior systemic therapy at the time the patient receives the E7 TCR cells.. Adverse events from prior therapy must have resolved to ≤grade 1 according to CTCAE Version 5.0 or have demonstrated clinical stability for the protocol.

⁃ Participants must be able to understand and be willing to sign the written informed consent document.

⁃ Participants must agree to participate in protocol Cancer Institute of New Jersey (CINJ) 192103 (Pro2021002307) for gene therapy long term follow up and in protocol CINJ 192002 (Pro2021000281) for biospecimen collection study.

• Note: Participants may have undergone minor surgical procedures with the past three weeks, as long as all toxicities have recovered to Grade 1 or less.