FH-WT1-E50 TCR T Cells With Azacitidine for the Treatment of Minimal Residual Disease Positive Acute Myeloid Leukemia

Inclusion Criteria for Leukapheresis: * LEUKAPHERESIS: Age 18 years or older at the time of enrollment * LEUKAPHERESIS: Confirmed diagnosis of AML that is not M3 subtype (acute promyelocytic leukemia \[APL\]) * LEUKAPHERESIS: Human leukocyte antigen (HLA) type HLA-A\*02:01 confirmed through HLA typing * LEUKAPHERESIS: Tissue confirmation of WT1 expression by immunohistochemistry. Confirmation of diagnosis must be or have been performed by internal pathology review of archival biopsy material or other pathologic material at Fred Hutch/University of Washington Medical Center (UWMC) * LEUKAPHERESIS: Capable of understanding and willing to provide informed consent * LEUKAPHERESIS: Fertile male and female participants must be willing to use an effective contraceptive method before, during, and for at least 4 months after the last FH-WT1-E50 TCR T infusion * LEUKAPHERESIS: Eastern Cooperative Oncology Group (ECOG) performance status of 0, 1, or 2 or Karnofsky Performance Status (KPS) ≥ 60% * LEUKAPHERESIS: No immediate plan for allogeneic stem cell transplantation: patients must not have a planned allogeneic hematopoietic stem cell transplant (HCT) within 8 weeks of leukapheresis. Patients may still be considered for HCT in the future but must not have a scheduled transplant at the time of enrollment due to factors including, but not limited to, donor availability, performance status, comorbidities, or patient preference. Patients who subsequently become candidates for HCT (e.g., donor identified or improvement in performance status) may proceed to transplant at the discretion of the treating physician without a mandated waiting period related to study participation * LEUKAPHERESIS: Creatinine clearance ≥ 30 ml/min by Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) or 24-hour urine clearance * LEUKAPHERESIS: Total bilirubin \< 3.0 mg/dL. Participants with suspected Gilbert syndrome may be included if total bilirubin (tBili) \> 3mg/dL but no other evidence of hepatic dysfunction * LEUKAPHERESIS: Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) \< 5 x upper limit of normal (ULN) * LEUKAPHERESIS: Participants 60 years of age or older are required to have left ventricular ejection fraction (LVEF) evaluation performed within 60 days prior to enrollment. LVEF may be established with echocardiogram or MUGA scan, and left ejection fraction must be ≥ 35%. Cardiac evaluation for other participants is at the discretion of the treating physician Inclusion Criteria at Start of Treatment: * START OF TREATMENT: Presence of Measurable Residual Disease (MRD) after induction therapy at the time of screening. Patients must have achieved a morphologic remission (marrow that is at least 10% cellular with \< 5% blasts on morphologic review) with detectable MRD, regardless of incomplete recovery of neutrophil counts/less than 1,000/mm3 (CRi) or platelet counts less than 100,000/mm3 (CRp). Eligible remission-induction regimens include, but are not limited to, conventional induction chemotherapy (e.g., 7+3 or similar anthracycline/cytarabine-based regimens) and hypomethylating agent-based combinations (e.g., azacitidine/venetoclax). * MRD definition: * MRD by flow cytometry: defined by any abnormal myeloid blasts identified by flow cytometric analysis. In addition, for patients with NPM1-mutated disease, we will incorporate a clinically validated quantitative NPM1 MRD assay performed at Fred Hutch. For patients with FLT3-ITD-mutated disease, MRD assessment will include a clinically validated FLT3-ITD assay performed at Invivoscribe. * START OF TREATMENT: Participants must be willing to undergo serial tumor biopsies and/or aspirates for research purposes if safe and feasible at baseline (prior to first T cell infusion), 2-3 weeks after the first T cell infusion, and approximately 2 weeks +/- 1 week after the second infusion (if applicable) (these windows may vary due to manufacturing or clinical reasons). Should there be no marrow tissue that is accessible, participants will still be considered for participation, at the discretion of the investigator. Similarly, should an investigator determine that a marrow assessment cannot be performed safely for clinical reasons, those may be cancelled or rescheduled. Participants must be at least two weeks or five half lives (for small molecules) from last systemic treatment: At least 2 weeks must have passed since any: immunotherapy (for example, T cell infusions, immunomodulatory agents, interleukins, vaccines), or chemotherapy cancer treatment. At least five half-lives must have passed from treatment with small molecules or other investigational agents * START OF TREATMENT: ECOG performance status of 0, 1, or 2 or Karnofsky Performance Status (KPS) ≥ 60% * START OF TREATMENT: Creatinine clearance ≥ 30 ml/min by CKD-EPI or 24-hour urine clearance * START OF TREATMENT: Total bilirubin \< 3.0 mg/dL. Participants with suspected Gilbert syndrome may be included if tBili \> 3mg/dL but no other evidence of hepatic dysfunction. * START OF TREATMENT: Participants 60 years of age or older are required to have left ventricular ejection fraction (LVEF) evaluation performed within 60 days prior to enrollment. LVEF may be established with echocardiogram or MUGA scan, and left ejection fraction must be ≥ 35%. Cardiac evaluation for other participants is at the discretion of the treating physician * START OF TREATMENT: Participants with a history of chronic obstructive pulmonary disease (COPD), emphysema, or greater than 30 pack year smoking history should undergo pulmonary function tests (PFTs) and meet the following criteria: * Forced expiratory volume in 1 second (FEV1) ≥ 50% of predicted and carbon monoxide diffusing capacity (DLCO) (corrected) ≥ 40% of predicted will be eligible Exclusion Criteria for Leukapheresis: * LEUKAPHERESIS: Prior solid organ transplant or allogeneic hematopoietic stem cell transplant. Kidney transplant participants w