Ruxolitinib With Tacrolimus and Methotrexate for the Prevention of Graft Versus Host Disease in Pediatric and Young Adult Patients Undergoing Allogeneic Hematopoietic Cell Transplant for Acute Myeloid Leukemia, Acute Lymphoblastic Leukemia, or Myelodysplastic Syndrome

Inclusion Criteria: * Documented informed consent of the participant and/or legally authorized representative * Assent, when appropriate, will be obtained per institutional guidelines * Agreement to allow the use of archival tissue from diagnostic tumor biopsies * If unavailable, exceptions may be granted with study primary investigator (PI) approval * Age: 2-22 * Weight ≥25kg * Eastern Cooperative Oncology Group (ECOG) ≤ 2 * Performance status: Karnofsky ≥ 60% for patients ≥ 16 years old OR Lansky status ≥ 60% for patients \< 16 years old * Candidate for allogeneic bone marrow transplant with and available matched related donor (MRD) or an 8/8 matched unrelated donor (MUD) who is willing to donate bone marrow (BM) or mobilized peripheral blood stem cells * Note: Donor selection process will be in accordance with City of Hope (COH)-standard operating procedures (SOPs) (B.001.09 Allogeneic Cellular Therapy Product Donor Evaluation, Selection \& Consent), which follows Food and Drug Administration (FDA) guidelines for donation of hematopoietic stem/progenitor cells (HPCs) obtained from peripheral blood or bone marrow * Diagnosis of acute leukemia (acute myeloid leukemia \[AML\] or acute lymphoblastic leukemia \[ALL\]) in complete remission, or myelodysplastic syndrome (MDS) * Fully recovered from the acute toxic effects (except alopecia) to ≤ grade 1 from prior anti-cancer therapy * Women of childbearing potential (WOCBP): negative urine or serum pregnancy test. If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required (to be performed within 30 days prior to day 1 of protocol therapy) * Agreement by females and males of childbearing potential to use an effective method of birth control or abstain from heterosexual activity for the course of the study through at least 6 months after the last dose of protocol therapy * Childbearing potential defined as not being surgically sterilized (men and women) or have not been free from menses for \> 1 year (women only) Exclusion Criteria: * Autologous stem cell transplant within 1 year prior to day 1 of protocol therapy * Prior allogeneic transplantation * Chemotherapy, radiation therapy, biological therapy, immunotherapy within 14 days prior to day 1 of protocol therapy * Note: Conditioning regimen within 21 days prior to day 1 of protocol therapy is not considered as an exclusion criterion. * Note: Patients on maintenance chemotherapy with agents listed are not excluded * Herbal medications * History of allergic reactions attributed to compounds of similar chemical or biologic composition to study agent * History of active tuberculosis * Patients with history of thrombosis including but not limited to myocardial infarction (MI)/stroke and pulmonary embolism (PE)/deep vein thrombosis (DVT) within 6 months of enrollment * Active diarrhea due to inflammatory bowel disease or malabsorption syndrome * Clinically significant uncontrolled illness * Active, uncontrolled systemic infection (viral, bacterial, or fungal) requiring antibiotics * Known history of immunodeficiency virus (HIV) or hepatitis B or hepatitis C infection * Other active malignancy * Females only: Pregnant or breastfeeding * Any other condition that would, in the investigator's judgment, contraindicate the patient's participation in the clinical study due to safety concerns with clinical study procedures * Prospective participants who, in the opinion of the investigator, may not be able to comply with all study procedures (including compliance issues related to feasibility/logistics)