Inclusion Criteria:
* Male or female aged ≥ 18 years at the time of signing the informed consent.
* Eastern Cooperative Oncology Group (ECOG)-PS ≤ 2 at the time of the screening visit.
* Contraceptive use by male and female participants must be consistent with local regulations regarding the methods of contraception for those participating in clinical studies.
* Male Participants:
* A male participant must agree to use a highly effective contraceptive as detailed in Appendix 4 of this protocol during the intervention period and for at least 12 months after the last dose of study intervention and refrain from donating sperm during this period.
* Female Participants:
* A female participant 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) OR
* A WOCBP who agrees to follow the contraceptive guidance during the intervention period and for at least 12 months after the last dose of study intervention.
* Preparing to undergo allogeneic HCT for either of the following:
* AML
* MDS
* ALL
* Participants in the treatment arms must express HLA-A\*0201. Participants in the control arm may express any HLA type.
* Having the HA1+/- or HA-1+/+ (HA-1 positive) genotype to be eligible for TSC-100 treatment.
* Having the HA2+/- HA-2+/+ (HA-2 positive) genotype to be eligible for TSC-101 treatment.
* Having a haploidentical donor, MMUD, or MUD for HCT who is adequately HLA-matched by institutional standards and meets the donor inclusion criteria.
* Considered to be clinically indicated for haploidentical donor, MMUD, or MUD transplantation at the discretion of the treating investigator.
* Considered to be clinically indicated for RIC at the discretion of the treating investigator.
* Considered to be clinically indicated for peripheral blood stem cell transplantation at the discretion of the treating investigator.
* Organ function parameters for transplant eligibility are met per institutional standards.
* Capable of giving signed informed consent - which includes compliance with the requirements and restrictions listed in the ICF and in this protocol.
* Participants must provide consent for mandatory study procedures including bone marrow biopsy and blood sampling for research analyses in the ICF.
* Participants must agree to participate in long-term follow-up for up to 15 years post initial product treatment if they are enrolled in the study and receive the investigational Tcell infusion.
Donor Inclusion Criteria :
* Male or female aged ≥ 18 years at the time of signing the informed consent.
* Able to undergo peripheral blood stem cell (PBSC) collection and up to 2 rounds of leukapheresis (for TSC-100 or TSC101 manufacturing for treatment arms only, and f for stem cell collection for both treatment arms and the control arm).
* Donors matched to TSC-100 participants should be HA-1-/- (negative) and/or negative for all HLA-A\*02 alleles
* Donors matched to TSC-101 participants should be negative for all HLA-A\*02 alleles
* Capable of giving signed informed consent which includes compliance with the requirements and restrictions listed in the ICF and in this protocol.
Exclusion Criteria:
* Medical or psychological conditions that would make the participant an unsuitable candidate for cell therapy including another concurrent uncontrolled malignancy or active CNS disease.
* The presence of organ toxicities will not necessarily exclude participants from enrolling on the protocol at the discretion of the PI; however, a delay in the infusion of HA1/HA2 TCRT cells may be required at the discretion of the treating investigator
* Participants with levels of donor-specific HLA antibodies that are considered by the treating investigator to be high enough to warrant desensitization protocols and who have no alternate donors.
* Participants who meet inclusion criteria for TSC-101 but who are also positive for HLAA\*02:07.
* Participants with evidence of clinically significant infection or uncontrolled viral r reactivation of cytomegalovirus (CMV), Epstein-Barr virus (EBV), Adenovirus, BK virus (BKV), or human herpesvirus 6 (HHV-6).
* Participants with active 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 \< 3 months from study entry.
* Uncontrolled or symptomatic congestive heart failure.
* Prior allogeneic HCT.
* Participants who have a history of hypersensitivity to murine proteins.
* Enrollment on a concomitant trial with a novel investigational agent.
* Use of anti-thymocyte globulin, alemtuzumab, or other in vivo T-cell depleting agents from Day -14 through end of study.
Donor Exclusion Criteria :
* Donors for TSC-100 positive for any HLA-A\*02 allele would be excluded unless they are HA-1 negative. If donors with any HLA-A\*02 allele are considered for patients eligible for TSC-100, the donor would undergo HA-1 testing to ensure that the donor is HA-1 negative (40% probability).
* Donors for TSC-101 positive for any HLA-A\*02 allele are excluded regardless of HA- 2 status.
* Donors who test positive for any of the following: 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 risk of CreutzfeldtJakob disease or Zika virus infection using donor history questionnaires will also be excluded. Donors with evidence of past CMV or EBV infections will be allowed.
* Related donor residing outside of the United States of America (USA). If the donor screening, testing and leukapheresis can be performed at the same site where the participant is being treated, the donor is considered eligible.
