• Provision of a signed and dated, written informed consent form prior to any study specific procedures, sampling, and analyses.

• Submission of the tumor block or unstained slides from an excisional or core biopsy from nodal or extra-nodal lymphoma tissue (archived or newly obtained sample) is required for retrospective central confirmation of tumor histological subtype.

• Aged ≥ 18 years old.

• Participants must exhibit Eastern Cooperative Oncology Group (ECOG) performance status 0-2 with no deterioration over the previous 2 weeks.

• Predicted life expectancy ≥ 12 weeks.

• Participants must have histologically confirmed peripheral T-cell lymphoma by MD Anderson pathology review according to the 2016 revision of the World Health Organization classification of lymphoid neoplasms53. Eligible histological subtypes are restricted to the following:

‣ PTCL, not otherwise specified (PTCL, NOS) (the proportion of PTCL-NOS subtype will not exceed 30% of all enrolled)

⁃ Angioimmunoblastic T-cell lymphoma (AITL)

⁃ Follicular T cell lymphoma

⁃ PTCL with T follicular helper (TFH) phenotype

• Participants must have measurable disease according to the 2014 Lugano classification, which is defined as lymphomatous nodes, nodal masses, or other lymphomatous lesions are measurable in two diameters (longest diameter \[LDi\] and shortest diameter perpendicular to the LDi \[SDi\]) on CT scans, and also with LDi as below:

‣ A measurable node must have an LDi greater than 1.5 cm.

⁃ A measurable extranodal lesion should have an LDi greater than 1.0 cm.

• Participants must be treatment naïve with no prior systemic treatment for T-cell lymphoma (i.e., PTCL). Participants could be transplant eligible or ineligible upon their entries to this study.

• Adequate bone marrow reserve and organ system functions, as outlined below:

‣ Absolute neutrophil count (ANC) ≥ 1 ×109/L (≥0.5 ×109/L if documented bone marrow involvement with lymphoma) independent of growth factor support within 7 days of study entry.

⁃ Platelets ≥ 75 × 109/L (or ≥ 50 × 109/L if documented bone marrow involvement with lymphoma) independent of growth factor support or transfusion within 7 days of study entry.

⁃ Hemoglobin ≥ 8 g/dL

⁃ Total bilirubin ≤ 1.5 ×ULN if no liver involvement or ≤ 3 ×ULN in the presence of documented Gilbert's Syndrome (unconjugated hyperbilirubinemia) or liver involvement.

⁃ Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) ≤ 2.5 × ULN, or ≤ 5 ×ULN if with document hepatic involvement with lymphoma.

⁃ Creatinine ≤ 1.5 × ULN, OR calculated or measured creatinine clearance ≥ 50 mL/min as calculated by the Cockcroft-Gault method, or 24-hour measured urine creatinine clearance ≥ 50 mL/min.

• LVEF ≥ 50% assessed by ECHO or MUGA.

• Participants should have the ability and willingness to comply with the study and follow up.

• The effects of golidocitinib on the developing human fetus are unknown. For this reason and because JAK1 inhibitor agents as well as other therapeutic agents used in this trial are known to be teratogenic, women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation. This includes all female patients, between the onset of menses (as early as 8 years of age) and 55 years unless the participants presents with an applicable exclusionary factor which may be one of the following:

‣ Postmenopausal (no menses in greater than or equal to 12 consecutive months).

⁃ History of hysterectomy or bilateral salpingo-oophorectomy.

⁃ Ovarian failure (Follicle Stimulating Hormone and Estradiol in menopausal range, who have received Whole Pelvic Radiation Therapy).

⁃ History of bilateral tubal ligation or another surgical sterilization procedure.

• Approved methods of birth control are as follows: Hormonal contraception (i.e. birth control pills, injection, implant, transdermal patch, vaginal ring), Intrauterine device (IUD), Tubal Ligation or hysterectomy, Subject/Partner post vasectomy, Implantable or injectable contraceptives, and condoms plus spermicide. Not engaging in sexual activity for the total duration of the trial and the drug washout period is an acceptable practice; however periodic abstinence, the rhythm method, and the withdrawal method are not acceptable methods of birth control. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately.

• Women treated or enrolled on this protocol must agree to use adequate contraception prior to the study, for the duration of study participation, and 4 months after completion of golidocitinib administration. If female patients wish to mother children, they should be advised to arrange for freezing of eggs prior to the start of study treatment.

• Men treated or enrolled on this protocol must also agree to use adequate contraception prior to the study, for the duration of study participation, and 4 months after completion of golidocitinib administration. Men must refrain from donating sperm during their participation in the study and at least for 6 months after the last treatment. If male patients wish to father children, they should be advised to arrange for freezing of sperm samples prior to the start of study treatment.