Inclusion Criteria:  Patients must have histologically proven diagnosis of lymphoid malignancy according to World health organization (WHO) defined as:  a. Mature T cell lymphoma b. T-cell Prolymphocytic leukemia c. Aggressive NK-cell leukemia d. Adult T-cell leukemia/lymphoma e. Hepatosplenic T-cell lymphoma f. Subcutaneous panniculitis-like T-cell lymphoma g. Primary cutaneous gamma/delta T cell lymphoma h. Primary cutaneous CD8+ aggressive epidermotropic cytotoxic T-cell lymphoma i. Mantle cell lymphoma j. Diffuse large B cell lymphoma, NOS k. Primary mediastinal large B cell lymphoma l. High grade B cell lymphoma, NOS m. High grade B cell lymphoma with myc and bcl2 and/or bcl6 rearrangements  Disease specific eligibility:  Mature T cell lymphoma, T cell prolymphocytic leukemia, aggressive NK-cell leukemia, adult T-cell leukemia/lymphoma, hepatosplenic T-cell lymphoma, subcutaneous panniculitis-like T cell lymphoma, primary cutaneous gamma/delta T cell lymphoma, primary cutaneous CD8+ aggressive epidermotropic cytotoxic T-cell lymphoma: Patient must have progressed after one line of therapy and ineligible for hematopoietic stem cell transplantation ,or progressed on two lines of therapy with no available curative options per investigator discretion. Mantle cell lymphoma: Patients must have progressed after at least two line of therapy with no available options that would provide clinical benefit per investigator discretion. Patients with prior Chimeric Antigen Receptor T cell (CART cells) therapy are allowed . Diffuse large B cell lymphoma NOS, primary mediastinal large B cell lymphoma, high grade B cell lymphoma NOS, high grade B cell lymphoma with myc, bcl2 and/or bcl6 rearrangements: Patients must have progressed on at least two lines of therapy with no available options that would provide clinical benefit per investigator discretion. Patients with prior Chimeric Antigen Receptor T cell (CART cells) therapy are allowed. Patients must have measurable disease with a lymph node or tumor mass > 1.5 cm in at least one dimension as assessed by computed tomography (CT) Patients must be ≥ 18 years of age. Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 1 (corresponds to Karnofsky Performance Status [KPS] ≥ 80%). Patients must have adequate organ and marrow function as defined in protocol.  Willingness to avoid pregnancy or fathering children based on the following criteria: a. Woman of non-childbearing potential (ie, surgically sterile with a hysterectomy and/or bilateral oophorectomy OR ≥ 12 months of amenorrhea and at least 45 years of age). b. Woman of childbearing potential who has a negative serum pregnancy test at screening and who agrees to take appropriate precautions to avoid pregnancy (with at least 99% certainty) from screening through safety follow-up. Permitted methods that are at least 99% effective in preventing pregnancy (see Appendix A) should be communicated to the subject and their understanding confirmed.  c. Man who agrees to take appropriate precautions to avoid fathering children (with at least 99% certainty) from screening through at least 93 days after the last dose of study treatment. Permitted methods that are at least 99% effective in preventing pregnancy  Exclusion Criteria:  History of central nervous system lymphoma (either primary or metastatic). Allogeneic stem cell transplant within the last 6 months, or autologous stem cell transplant within the last 3 months before the date of the first dose of study treatment. Active graft-versus-host disease Ongoing treatment with chronic immunosuppressants (e.g., cyclosporine) or systemic steroids >20 mg of prednisone (or equivalent) once daily (QD) Receipt of anticancer medications or investigational drugs within the following intervals before the first dose of study treatment:a. < 6 weeks for mitomycin-C or nitrosoureas.b. < 4 weeks for immunotherapy.c. < 3 weeks for radiotherapy. d. < 2 weeks for any investigational agent or other anticancer medications or equal to 5 half lives of the investigational drug, whichever is longer. Prior CART cells therapy within 90 days of enrollment or if they have not recovered from CART cells therapy toxicity to grade 1 or less. Inadequate recovery from toxicity and/or complications from a major surgery before the date of the first dose of study treatment. Prior treatment-related toxicities have not resolved to NCI CTCAE v5 ≤ Grade 1 before the date of the first dose of study treatment except for stable chronic toxicities (Grade ≤ 2) not expected to resolve (eg, stable Grade 2 peripheral neurotoxicity). Concurrent anticancer therapy (eg, chemotherapy, radiation therapy, surgery, immunotherapy, biologic therapy, hormonal therapy, investigational therapy, or tumor embolization). Use or expected use during the study of any prohibited medications, including potent CYP3A4 inhibitors or inducers within 14 days or 5 half-lives (whichever is longer) before the date of study treatment administration (see appendix 11.1) in addition to excluding patients on CYP3A inducers. Significant concurrent, uncontrolled medical condition, including, but not limited to, renal, hepatic, hematological, GI, endocrine, pulmonary, neurological, cerebral, or psychiatric disease. Current or previous other malignancy within 3 years of study entry, except cured basal or squamous cell skin cancer, superficial bladder cancer, prostate intraepithelial neoplasm, carcinoma in situ of the cervix, or other noninvasive or indolent malignancy without PI approval. History of stroke or intracranial hemorrhage within 6 months of the date of study treatment administration. Chronic or current active infectious disease requiring systemic antibiotics, antifungal, or antiviral treatment or exposure to a live vaccine within 30 days of study treatment. Known HIV infection or positivity on immunoassay. Active cytomegalovirus (CMV) or Epstein-Barr virus (EBV) infection (i.e., subjects with detectable viral load) Hepatitis B (HBV) or hepatitis C (HCV) infection: Subjects with a positive hepatitis B surface antigen [HBsAg] or hepatitis C antibody [HCV Ab] will be excluded. Subjects with a positive hepatitis B core antibody (HBcAb) must have negative hepatitis B virus (HBV) deoxyribonucleic acid (DNA) to be eligible, must receive prophylaxis with entecavir (or equivalent) concomitant with duvelisib treatment, and must be periodically monitored for HBV reactivation by institutional guidelines. Investigators who strongly believe that a positive HBcAb is false due to passive immunization from previous immunoglobulin infusion therapy should consider the risk-benefit for the patient given the potential for reactivation History of tuberculosis treatment within the 2 years prior to randomization Clinically significant cardiac disease, including unstable angina, acute myocardial infarction, and/or cardiac conduction issues within 6 months of the date of study treatment administration. Current New York Heart Association Class II to IV congestive heart failure or uncontrolled arrhythmia. Presence of an abnormal ECG that is clinically meaningful. Screening QTc interval 450 milliseconds is excluded (corrected by Fridericia). In the event that a single QTc is > 450 milliseconds, the subject may enroll if the average QTc for 3 ECGs is < 450 milliseconds. Unable to swallow and retain oral medication, malabsorption syndrome, disease significantly affecting GI function, total resection of the stomach or small bowel, ulcerative colitis, symptomatic inflammatory bowel disease, or partial or complete bowel obstruction. Unable to receive prophylactic treatment for pneumocystis, herpes simplex virus (HSV), or herpes zoster (VZV) at screening Known hypersensitivity or severe reaction to duvelisib or CC-486 or its excipients (refer to the IB). History of serious allergic reactions including anaphylaxis and toxic epidermal necrolysis. Currently pregnant or breastfeeding Any condition that would, in the investigator's judgment, interfere with full participation in the study, including administration of study treatment and attending required study visits; pose a significant risk to the subject; or interfere with interpretation of study data. Inability to comprehend or unwilling to sign the informed consent form