Phase 1/1b Study of T-allo10 Infusion After HLA-Partially Matched Related or Unrelated TCR αβ+ T-cell/ CD19+ B-cell Depleted Allogeneic Hematopoietic Stem Cell Transplantation (αβ Depleted-HSCT) in Children and Young Adults Affected by Hematologic Malignancies

Inclusion Criteria prior to enrollment: * 1\. Age \> 1 months (with minimum weight of 10 Kg) and \< 45 years. * 2\. Patients deemed eligible for allogeneic HSCT under the originating study, NCT 04249830 * 3\. Patients with life-threatening hematological malignancies for which HSCT has been recommended: 1. High-risk ALL in 1st CR, ALL in 2nd or subsequent CR; 2. High-risk AML in 1st CR, AML in 2nd or subsequent CR; 3. Myelodysplastic syndrome; 4. JMML (Juvenile myelomonocytic leukemia); 5. Non-Hodgkin lymphomas in 2nd or subsequent CR; 6. Other hematologic malignancies eligible for stem cell transplantation per institutional standard. * 4\. All subjects ≥ 18 years of age must be able to give informed consent, or adults lacking capacity to consent must have a LAR available to provide consent. For subjects \<18 years old their LAR (i.e. parent or guardian) must give informed consent. Pediatric subjects will be included in age appropriate discussion and verbal assent will be obtained for those \> 7 years of age, when appropriate. Inclusion criteria prior to T-allo10 infusion: 1. Patient already received αβdepleted-HSCT and has myeloid engraftment. 2. Absence of active grade II aGvHD requiring \>0.5 mg/Kg of steroids or any diagnosis of grade III/IVaGvHD. Exclusion Criteria prior to MNC collection for Tallo-10 manufacturing.: 1. Not eligible to receive HSCT on NCT04249830 2. Received another investigational agent within 30 days of enrollment. 3. Pregnancy (positive serum or urine beta-HCG) within 7 days of MNC donation. 4. Patient or donor is not willing or able to undergo an additional non-mobilized apheresis for collection of MNC prior to donation of cells for participation in NCT04249830.