Inclusion Criteria：
1. Subject voluntarily sign informed consent and are willing and able to comply with all trial requirements;
2. Age is 18-75 years old and gender is not limited;
3. Malignancy cells in bone marrow or peripheral blood are Cluster of Differentiation 19 - positive(CD19+) detected by flow cytometric analysis;
4. 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.
5. Morphological examination of bone marrow cells showed the proportion of primitive and naive lymphocytes was\> 5%;
6. No Hematopoietic Stem Cell Transplantation(HSCT) within 6 months before enrollment;
7. 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.
8. More than 12 weeks of expected survival period
9. Baseline Eastern Cooperative Oncology Group(ECOG) score was 0-1;
10. 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;
11. 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;
12. 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.
Exclusion Criteria：
1. Subjects with active cerebrospinal fluid malignant cells or brain metastases, or subjects with active central nervous system (CNS) lymphoma, or CNS leukaemia;
2. Subjects with a history of active CNS disease, such as seizures, cerebrovascular ischemia / hemorrhage, dementia, cerebellar disease, or any autoimmune disease associated with CNS involvement;
3. Subjects who have received other study drugs within 30 days before screening, or are still in the washout period;
4. Patients who have previously received any anti-CD19 / anti-Cluster of Differentiation 3(CD3) therapy or any other anti-CD19 therapy (except for those with normal T cell numbers and function and with CD19-positive tumors);
5. Patients who have been previously treated with any gene therapy product, including Chimeric Antigen Receptor T(CAR-T) therapy (except patients who do not have CAR-T cells in vivo and have normal T cell number and function and are with CD19 positive tumors);
6. Subjects with radiation therapy within 2 weeks prior to the infusion;
7. Subjects with active hepatitis B (defined as Hepatitis B Virus(HBV) DNA test value\> 500 IU / mL) or hepatitis C (HCV RNA positive); subjects with HIV positive or treponema pallidum positive;
8. Subjects with uncontrolled acute life-threatening bacterial, viral, or fungal infection (e. g. positive blood culture 72 hours before infusion);
9. Subjects with unstable angina pectoris and / or myocardial infarction within the 6 months prior to screening;
10. Subjects with concurrent or previously diagnosed with other malignancies, except for the patients under following conditions:
* Well treated basal cells, papillary thyroid carcinoma, squamous cell carcinoma (adequate wound healing is required before enrollment into this study);
* Carcinoma in situ of cervical cancer or breast cancer, after curative treatment, showed no signs of recurrence for at least 3 years before the study;
* The primary malignancy has been completely removed and is in complete remission for 5 years.
11. Arrhythmic subjects without medical management control;
12. Subjects receiving oral anticoagulation within 1 week before JY231 injection infusion;
13. Having active neurological autoimmune or inflammatory conditions (such as Guillain-Barre syndrome, amyotrophic lateral sclerosis);
14. Female subjects in pregnant or lactating, or women with planned pregnancy within 2 years after JY231 infusion or male partner with planned pregnancy within 2 years after JY231 infusion;
15. Subjects with taboo study procedures or other medical conditions that may put them at unacceptable risk according to the investigator's judgment and / or clinical criteria.
Other conditions that the investigator believes that the subjects should not be enrolled in this clinical trial, such as poor compliance.
