Inclusion Criteria:  Volunteer to participate in this study and sign the informed consent form. Age ≥18 and ≤75 years, regardless of gender.  Unresectable locally advanced, recurrent or metastatic gastric cancer (including gastric-esophageal junction adenocarcinoma) confirmed by histopathology and/or cytology; patients have received at least the first-line platinum or taxane based treatment (Patients who have progressed or recurred during neoadjuvant/adjuvant therapy or within 6 months after completion of treatment can participate. In this case, neoadjuvant/adjuvant therapy can be counted as one previous (1st-line) therapy); for each cohort in part 2, HER2-positive patients must also include trastuzumab or trastuzumab analog in the previous 1st-line therapy.  Part 1 Progression on or after ≥ 1st-line treatment, HER2 positive. Part 2 Cohort A: Progression on or after 1st-line treatment, HER2 positive; Cohort B: Progression on or after ≥ 2nd-line of treatment, HER2 positive; Cohort C: Progression on or after ≥ 1st-line treatment, low expression of HER2; Cohort D: Progression on or after ≥ 1st-line treatment, HER2 low expression or HER2 positive.  HER2 positive expression is defined as IHC 3+ or IHC 2+ with ISH test positive; HER2 low expression is defined as IHC 1+ or IHC 2+ with ISH test negative.  Eastern Cooperative Oncology Group (ECOG) score of 0-1, and life expectancy ≥ 3 months.  The function of major organs must meet the following criteria within 7 days before enrollment (Have not received blood transfusion, EPO, G-CSF or other medical supportive treatment within 14 days before the first dose of study drug):  Absolute neutrophil count (ANC) ≥1.5×109 /L, Platelet ≥100×109 /L; Hemoglobin ≥90 g/L or ≥5.6 mmol/L; International normalized ratio (INR) or prothrombin time (PT) ≤1.5×ULN; Activated Partial Thromboplastin Time (APTT) ≤1.5×ULN; Creatinine clearance rate ≥30 mL/min (Calculated by Cockcroft-Gualt formula); Total bilirubin ≤1.5×ULN, or ≤3×ULN for patients with Gilbert's syndrome or liver metastasis; Aspartate aminotransferase (AST) and Alanine aminotransferase (ALT) ≤2.5×ULN, or ≤5×ULN for patient.  At least one measurable lesion at baseline per RECIST v1.1. Women of childbearing age must have a negative pregnancy test prior to study entry. Female and male patient of childbearing age must agree to take adequate contraceptive measures during the entire study period and through at least 6 months after the last dose of study drug.  Exclusion Criteria:  Pregnant or breastfeeding women. Has not recovered from adverse reactions caused by previous anti-tumor treatments to ≤ grade 1 or baseline (refer to NCI CTCAE 5.0), except for alopecia, pigmentation and other toxicity judged no safety risk by the investigator. Patients who have previously received trastuzumab or trastuzumab analogues and have related toxicity, resulting in permanent discontinuation. Patients with history of allergy to any components (trastuzumab analogues, MMAE, sodium citrate dihydrate, citric acid monohydrate, polysorbate 20, sucrose, etc.) of DP303c. Patients with brain or pia mater metastasis; except for patients with central nervous system (CNS) metastases in the following conditions: untreated but asymptomatic, or progression-free status in imaging evidence for at least 4 weeks after treatment and not requiring hormone therapy for at least 4 weeks. Patients with pleural effusions or ascites that are difficult to control (the frequency of percutaneous drainage is more than once a week, or continuous drainage daily volume is ≥500 mL). The patient had acute and chronic gastrointestinal bleeding with hematemesis or melena within 4 weeks before the first administration of study drug (except for patients with only the fecal occult blood test positive, but without visible bleeding such as melena or hematemesis). Patients with gastrointestinal obstruction. Patients with dyspnea at rest induced by complications of advanced malignant tumors or need for continuous oxygen therapy. History of any other malignant tumors within five years (except for skin basal cell carcinoma, skin squamous cell carcinoma, superficial bladder cancer, local prostate cancer, cervical cancer in situ and other malignant tumors that have been radically removed and have not recurred). History of (non-infectious) interstitial pneumonia/pulmonary disease that requires steroid treatment, or current interstitial pneumonia/pulmonary disease, or suspected interstitial pneumonia/pulmonary disease that cannot be excluded by imaging examination; except for patients with radiation pneumonitis without clinical symptoms after 3 months of radiotherapy. Patients who currently have corneal diseases that require medication or surgical intervention, or have a history of serious corneal diseases, or are unwilling to stop wearing contact lenses during the study.  History of congestive heart failure, unstable angina pectoris, arrhythmia.  Patients with the following cardiac function defects at the time of enrollment:  New York Heart Association (NYHA) heart function classification is level III or IV; Uncontrolled angina, congestive heart failure or myocardial infarction within 6 months before enrollment; Left ventricular ejection fraction (LVEF) <50% or lower limit of normal in echocardiogram (ECHO) or multi-gate detection scan (MUGA); Average adjusted QT interval prolongation (male>450 ms, female>470 ms), QT interval corrected by Fridericia's formula (QTcF). The cumulative amount of previous exposure to anthracyclines has reached the following doses: doxorubicin or liposomal doxorubicin>500 mg/m2; epirubicin>900 mg/m2; mitoxantrone>120 mg/m2. Peripheral neuropathy ≥ grade 2 before entry (refer to NCI CTCAE 5.0). Uncontrollable electrolyte imbalances include hypokalemia, hypocalcemia or hypomagnesemia (refer to NCI CTCAE 5.0, ≥2 grade). Patients with active hepatitis B or C (HBsAg positive, with HBV DNA positive, and the ALT continues to be higher than the upper limit of normal, without other causes of ALT elevation; HCVAb positive with HCV RNA higher than the upper limit of normal). Test positive for HIV or syphilis. Patients have used strong CYP3A4 inhibitors (drugs that increase the AUC of specific CYP substrates ≥ 5 times, or CYP3A4 strong inducers with a washout period less than 5 half-lives before the first dose of study drug. Patients underwent major surgery within 4 weeks and did not fully recover before the first dose of study drug. Chemotherapy, radiotherapy, immunotherapy and other anti-tumor treatments within 4 weeks before the first dose of study drug, within 2 weeks for Chinese medicine treatment with anti-tumor indications or local palliative radiotherapy for bone metastasis and pain relief; or within 5 half-lives for oral fluorouracil and small molecule targeted drugs. Patients have received other clinical trial drugs within 4 weeks before the first dose of study drug. Have previously received antibody drug conjugate targeting HER2. Other serious or uncontrollable diseases or conditions that may affect the evaluation of the primary endpoint or the investigator believes that participation in this study may bring risks to the patient.