There're 2 parts in this interventional study:

1. The goal of phase Ib trial is to evaluate the safety and tolerability of AK130 in combination with AK112 therapy for the purpose of observing the incidence of dose limit toxicity (DLT) as well as the confirmation of maximum tolerable dose (MTD) in the treatment of advanced biliary tract cancer (BTC), so as to determine the recommended phase 2 dose (RP2D) in the second part of the trial.
2. The goal of phase II trial is to evaluate the safety and efficacy of AK112 in combination with AK130 therapy or monotherapy in the treatment of advanced BTC.

Inclusion Criteria:

1. Be able and willing to provide written informed consent.
2. Have a life expectancy of at least 3 months.
3. Have an Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1.
4. Subjects with histologically and/or cytologically confirmed advanced or metastatic biliary tract malignancies (including only intrahepatic cholangiocarcinoma, extrahepatic cholangiocarcinoma, and gallbladder carcinoma; excluding ampullary carcinoma), who have experienced treatment failure following prior first-line systemic therapy.
5. According to RECIST v1.1, there is at least one untreatable measurable lesion, or a measurable lesion with clear imaging progression after local treatment, suitable for repeated and accurate measurement.
6. Has adequate organ function.
7. All subjects of reproductive potential must agree to use an effective method of contraception, as determined by the Investigator, during and for 120 days after the last dose of study treatment.
8. Able to to comply with all requirements of study participation (including all study procedures).

Exclusion Criteria:

1. Except for BTC, the subjects had other malignant tumors within the 3 years prior to enrollment. Subjects with other malignant tumors that have been cured through local treatment are not excluded, such as basal or cutaneous squamous cell carcinoma, superficial bladder cancer, cervical or breast cancer in situ.
2. There is central nervous system (CNS) metastasis, spinal cord compression, or meningeal metastasis.
3. There are pleural effusion, pericardial effusion, or ascites with clinical symptoms or requiring repeated drainage.
4. Prior administration of any immunotherapy targeting immune mechanisms other than PD-1/PD-L1 inhibitors.
5. There is a history of non infectious pneumonia that requires systemic glucocorticoid treatment.
6. History of severe bleeding tendency or coagulation dysfunction.
7. Previous history of myocarditis, cardiomyopathy, and malignant arrhythmia.
8. Any arterial or severe venous thromboembolism events, transient ischemic attacks, cerebrovascular accidents, hypertensive crises, or hypertensive encephalopathy occurred within 6 months prior to the first administration of medication.
9. Pregnant or lactating female subject.
10. Any prior or concurrent disease, treatment, or laboratory test abnormality that may confuse study results, affect subjects' full participation in the study, or may not be in their best interest to participate.