• Subject voluntarily sign informed consent and are willing and able to comply with all trial requirements;

• Age is 18-75 years old and gender is not limited;

• Malignancy cells in bone marrow or peripheral blood are Cluster of Differentiation 19 - positive(CD19+) detected by flow cytometric analysis;

• Meet the clinical criteria for relapsed or refractory B-cell lymphoma, including: indolent lymphoma (iNHL), such as follicular lymphoma (FL) and marginal zone lymphoma (MZL); aggressive B-cell lymphoma, like diffuse large B-cell lymphoma (DLBCL), primary mediastinal large B-cell lymphoma (PMBCL), transformed follicular lymphoma (TFL), and T-rich lymphocyte-bearing large B-cell lymphoma (TCRBCL), or have a diagnosis of acute B-lymphocytic leukemia (B-ALL) and meet one of the following conditions:

‣ Refractory B-ALL: those who did not achieve complete remission after 2 courses of standard induction regimen chemotherapy, or those who did not achieve complete remission after first-line or multi-line salvage chemotherapy;

⁃ Relapsed B-ALL: relapse within 12 months after first remission, or relapse after first-line / multi-line salvage chemotherapy;

⁃ Relapse after autologous or allogeneic hematopoietic stem cell transplantation; In addition, patients with Philadelphia chromosome positive (Ph +) should be relapsed after at least two tyrosine kinase inhibitors (TKI) treatment, or they could not tolerate TKI therapy, or have a t315i mutation, resistant to TKI drugs.

• Morphological examination of bone marrow cells showed the proportion of primitive and naive lymphocytes was\> 5%;

• No Hematopoietic Stem Cell Transplantation(HSCT) within 6 months before enrollment;

• At least one measurable lesion was imaging for relapsed or refractory B cell lymphoma, long diameter of\> 15mm, or extranodal lesion of\> 10mm, along with a positive Positron Emission Tomography - Computed Tomography(PET-CT) examination.

• More than 12 weeks of expected survival period

• Baseline Eastern Cooperative Oncology Group(ECOG) score was 0-1;

⁃ Adequate organ function (criteria regarding liver and kidney function can be moderately relaxed):

∙ Glutamic aminotransferase (ALT) ≤3 times upper limit of normal (ULN);

‣ Grass aminotransferase (AST) ≤3 times ULN;

‣ Total bilirubin ≤1.5 times ULN;

‣ Serum creatinine ≤ 1.5 times ULN, or creatinine clearance ≥ 60 mL/min;

‣ Indoor oxygen saturation ≥ 92%;

‣ Left ventricular ejection fraction (LVEF)≥55%, echocardiography confirmed no pericardial effusion and no clinically significant ECG findings;

‣ There is no clinically significant pleural effusion;

⁃ Adequate bone marrow reserve without transfusion, defined as:

∙ Absolute neutrophil count (ANC)\>1.000 / mm3;

‣ Absolute lymphocyte count (ALC)≥ 300 / mm3;

‣ Platelet≥50.000/mm3;

‣ Hemoglobin\>8.0 g/dl;

⁃ Subjects using the following drugs need to meet the following conditions:

∙ Steroids: The therapeutic dose of steroids must be stopped 72 hours before JY231 infusion. However, physiological alternative doses of steroids are allowed;

‣ Immunosuppression: Any immunosuppressive drug must be stopped at ≥4 weeks prior to enrollment;

‣ Antiproliferative therapy other than lymphodepletion chemotherapy within two weeks of infusion;

‣ Cluster of Differentiation 20(CD20) antibody-related therapy must be stopped within 4 weeks before infusion or 5 half-lives after the CD20 antibody;

‣ CNS disease prophylaxis must be stopped 1 week before JY231 infusion (e. g. intrathecal methotrexate).

• Reproductive men, sexual partners ensure effective contraception; fertile women, adopted effective contraception and agreed to use contraception throughout the study period.