Phase I Study of Ex Vivo Expanded/Activated Gamma Delta T-cell Infusion Following Haploidentical Hematopoietic Stem Cell Transplantation and Post-transplant Cyclophosphamide

Inclusion Criteria: The following criteria are used to enroll patients in the study before transplant. * Patients with neoplastic hematological disorders with indication of allogeneic transplant according to the National Comprehensive Cancer Network (NCCN) or other standard guidelines as follows: * Acute myeloid leukemia \[AML\] in morphologic complete remission with intermediate/high-risk features (per NCCN criteria) or relapsed disease * Chronic myeloid leukemia \[CML\] in any chronic phase. * Myelodysplastic syndrome \[MDS\] with intermediate/high risk features or refractory disease (with bone marrow blast count \<10%). * Acute lymphoblastic leukemia \[ALL\] in morphologic complete remission with high-risk features or relapsed disease. * Negative test for donor-specific antibody within 28 days of starting conditioning regimen. * Age Criteria: 19-65 years. * Organ Function Criteria: The following organ function testing should be done within 35 days before study registration. * Cardiac: Normal left ventricular ejection fraction (LVEF) (50% or above) as measured by MUGA or Echocardiogram. * Pulmonary: FVC, FEV1 and DLCO (corrected) should be 50% or above of expected. * Renal: serum creatinine level to be \<2 mg/dl AND estimated (Cockcroft-Gault formula) or measured (takes priority if done) creatinine clearance (CrCl) must be equal or greater than 70 mL/min/1.73 m2. * Hepatic: serum bilirubin 1.5 upper limit of normal (ULN), Aspartate transaminase (AST)/alanine transaminase (ALT) 2.5 ULN, and alkaline phosphatase 2.5 ULN. * Performance status: Karnofsky performance score (KPS) or Lansky score: ≥80. * Hematopoietic cell transplant comorbidity index (HCT-CI) \<3. Exception may be made on individual cases after discussion with the primary investigator. * Consent: All patients must be informed of the investigational nature of this study and given written informed consent in accordance with institutional and federal guidelines. The following criteria are required within 48 hours prior to infusion of the EAGD T cell product. * Absence of uncontrolled infection with sepsis syndrome (e.g persistent positive blood culture). * NO hemodynamic instability (due to sepsis or organ dysfunction) or circulatory volume overload. * NO clinically significant organ toxicity that are defined as follows: * Heart failure with subnormal LVEF or clinical fluid overload. * Elevated serum creatinine or subnormal creatinine clearance (either estimated or measured). * Elevated total bilirubin ≥1.5 upper normal level (unless indirect hyperbilirubinemia attributed to non-hepatic pathology), or elevated liver enzymes (ALT, AST, ALP) \>5 x ULN. * Hypoxemia requiring oxygen therapy * NO acute graft versus host disease (any grade). * Neutrophil engraftment. Exclusion Criteria: * Non-compliant patients. * No appropriate caregivers identified. * Uncontrolled medical or psychiatric disorders which may preclude patients to undergo clinical studies (Discretion of the attending physician). * Active central nervous system (CNS) neoplastic involvement. * Morbid obesity with body mass index \>35 (borderline cases may be considered on case-by-case basis after discussion with the primary investigator). * Patients with known allergy to DMSO. * HIV1 (Human Immunodeficiency Virus-1) or HIV2 positive. * Pregnant or breastfeeding women.