A Study of T-Cell Receptor Engineered Donor T Cells in Subjects Undergoing Allogeneic Peripheral Blood Stem Cell Transplantation

Subject Inclusion Criteria: 1. Patient aged ≥ 18 years at the time of signing informed consent. 2. Karnofsky Performance Status (KPS) ≥50 at the time of the screening visit. 3. Undergoing first allo-HCT with a diagnosis of: * AML with bone marrow blasts \< 5%, absence of circulating blasts, and absence of extramedullary disease. * MDS 4. Must express HLA-A\*02:01 as determined by pre-transplant institutional SOC work-up to be eligible for the treatment arm. 5. Must have the HA-2 positive genotype to be eligible for the treatment arm. 6. Undergoing RIC HCT using a haplo donor or MMUD. * Donors for treatment-arm subjects must be HLA-A\*02-negative. * Donors for control-arm subjects do not have to be HLA-A\*02-negative. 7. Undergoing use of PTCy for GvHD prophylaxis at standard doses. 8. Use of peripheral blood stem cell source. 9. Organ function parameters for transplant eligibility are met per institutional standards. Where organ function may fall outside of institutional standard for transplant, and patient is still proceeding to transplant, the case should be reviewed and approved by the MedicalMonitor. 10. Patient or legally authorized representative (LAR) capable of giving signed informed consent and willingness to comply with the requirements and restrictions listed in the informed consent form (ICF) and clinical protocol. 11. Agrees to participate in long-term follow-up (LTFU) for up to 15 years post the final infusion of TSC-101 if they receive a TSC-101 infusion. 12. Contraceptive use by male and female subjects must be consistent with local regulations regarding the methods of contraception for those participating in clinical studies. At a minimum: * A male subject must agree to use a highly effective contraceptive during the intervention period and for at least 12 months after the last TSC-101 infusion and refrain from donating sperm during this period. * A female subject is eligible to participate if she is not pregnant, not breastfeeding, and at least one of the following conditions applies: * Not a woman of childbearing potential (WOCBP) as defined in Appendix 2 OR * A WOCBP who agrees to follow the contraceptive guidance in Appendix 2 during the intervention period and for at least 12 months after the last TSC-101 infusion. Subject Exclusion Criteria: Patients are excluded from the study if any of the following criteria apply: 1. Potential treatment-arm patient is positive for HLA-A\*02:07. • Patients considered for the control arm can be positive for HLA-A\*02 (including HLA-A\*02:07). 2. For patients with AML: those in third complete remission (CR3) or greater, partial remission, or with active AML disease. 3. If patient required hemodialysis or mechanical ventilation within 3 months prior to enrollment, circumstances must be discussed with the Sponsor Medical Monitor. 4. Prior allo-HCT. 5. Use of anti-thymocyte globulin (ATG), alemtuzumab, or other in vivo or ex vivo T-cell depleting agents from Day -14 (pre-HCT) through end of study (EOS). Corticosteroids and maintenance therapies may be allowed under certain circumstances. 6. History of hypersensitivity to murine proteins. 7. Enrollment in a concomitant study with an investigational agent. All other concomitant trials must be reviewed and approved by the Medical Monitor. 8. Cardiac disease, defined as: * Uncontrolled or symptomatic angina within the past 3 months. * History of clinically significant arrhythmias (such as ventricular tachycardia, ventricular fibrillation, torsades de pointes). Atrial fibrillation with controlled ventricular response on treatment is not an exclusion. * Myocardial infarction \< 6 months from study entry. * Uncontrolled or symptomatic congestive heart failure. * Cardiac ejection fraction at rest of less than 40% or shortening fraction of less than 22% by echocardiogram or radionuclide scan (multi-gated acquisition \[MUGA\] scan). 9. Medical or psychological conditions that would make the patient an unsuitable candidate for participation on a cell therapy trial, including active central nervous system disease and/or prior malignancy(s) within the last 3 years, except: * Lobular breast carcinoma in situ, fully resected basal cell or squamous cell carcinoma of skin or treated cervical carcinoma in situ will be allowed. Cancer treated with curative intent ≥ 3 years previously will be allowed Donor Inclusion Criteria: 1. Male or female ≥ 50 kg and aged ≥ 16 years at the time of signing informed consent who meet the criteria to donate as per the institutional SOC. 2. Capable of giving signed informed consent, or assent/parental consent per institutional SOC, which includes compliance with the requirements and restrictions listed in the ICF and in this protocol. 3. For treatment-arm donors: able to undergo peripheral blood stem cell (PBSC) collection and at least 2 rounds of leukapheresis (for both TSC-101 manufacturing and the stem cell collection for HCT). 4. For treatment-arm donors: negative for all HLA-A\*02 alleles • Donors for control-arm subjects do not have to be negative for HLA-A\*02 alleles. Donor Exclusion Criteria: 1. Donors for control-arm subjects who do not meet institutional standards for donor selection. 2. Donors for treatment-arm subjects: * Who test positive for any of the following: human immunodeficiency virus (HIV)-1, HIV-2, human T-lymphotropic virus (HTLV)-1, HTLV-2, seropositive or with active hepatitis B or hepatitis C virus infection, syphilis, West Nile virus through central lab testing. Donors who screen positive for Creutzfeldt Jakob disease using donor history questionnaires will also be excluded. Donors with evidence of past cytomegalovirus (CMV) or Epstein-Barr virus (EBV) infections will be allowed. * For whom the treating Investigator deems subject level donor-specific HLA antibodies are high enough to warrant treatment with desensitization protocols.