* Dose escalation Phase and Dose expansion Phase Inclusion Criteria:
1. Written informed consent by the participants or the participant's legally authorized representative prior to screening.
2. Participants with Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 1 at study enrollment and an estimated life expectancy of at least 3 months.
3. Disease must have at least 1 measurable lesion by Response Evaluation Criteria in Solid Tumors (RECIST) version 1.1. Tumor lesions situated in a previously irradiated area are not considered measurable unless there has been demonstrated progression in the lesion. Imaging tests outside the screening period are valid if performed not more than 2 weeks before consent signature and otherwise fulfil protocol criteria.
4. Participants with adequate organ function defined by the following:
Participants must not have required blood transfusion or growth factor support ≤ 14 days before sample collection at screening:
1. Absolute neutrophil count ≥ 1.5 × 109 /L.
2. Platelet count ≥ 100 × 109 /L.
3. Hemoglobin ≥ 9 g/dL.
4. Alanine aminotransferase and AST ≤ 2.5 × ULN or \< 5 × ULN if hepatic metastases present.
5. Serum total bilirubin ≤ 1.5 × ULN (or \< 3 × ULN for participants with Gilbert's syndrome).
6. Alkaline phosphatase ≤ 2.5 × ULN or \< 5 × ULN if bone metastases present.
7. Prothrombin time ≤ 1.5 × ULN.
8. International normalized ratio (INR) ≤ 2.0 or activated partial thromboplastin time (aPTT) ≤ 1.5 × ULN. Exception: INR 2 to ≤ 3 is acceptable for participants on a stable dose of anticoagulants.
9. Estimated creatinine clearance \> 50 mL/min according to the Cockcroft Gault formula
5. Participants with highly effective contraception (that is, methods with a failure rate of less than 1% per year) for both male and female participants if the risk of conception exists.
* Dose escalation Phase specific Inclusion Criterion:
1. Participants with histologically or cytologically proven locally unresectable advanced or metastatic solid tumors, which are refractory or intolerant to standard therapy or for which no standard therapy exists.
* Dose expansion Phase specific Inclusion Criteria:
1. Participants who have histologically or cytologically confirmed diagnosis of relapsed or refractory, locally unresectable advanced or metastatic NSCLC, HNSCC, ESCC, who received at least one line of systemic treatment including anti-PD-1 or anti-PD-L1 therapy.
2. Only participants who have evaluable PD L1 expression results are eligible.
3. NSCLC cohort:
* Documented histologically or cytologically squamous or non-squamous stage IV NSCLC.
* Documented evidence of tumors expressing PD L1 (TPS ≥ 1%) for the determination of PD L1 expression in NSCLC.
* No sensitive epidermal growth factor receptor (EGFR) mutation and anaplastic lymphoma kinase (ALK) rearrangement.
* No known actionable genomic alterations of ROS1 rearrangement, BRAF V600E mutation, MET mutation, NTRK1/2/3 gene fusion, and/or RET rearrangement.
4. HNSCC cohort:
• Documented histologically or cytologically squamous cell carcinoma of the head and neck. Nasopharynx is excluded.
• Refractory or intolerant to platinum based chemotherapy or concurrent chemoradiation.
* PD L1 expression: Documented evidence of Combined Positive Score (CPS) ≥ 1 for PD L1.
5. ESCC cohort:
* Documented histologically or cytologically squamous carcinoma.
* PD L1 expression: Documented evidence of CPS ≥ 1 for PD L1.
* Dose escalation Phase and Dose expansion Phase Exclusion Criteria:
1. Participants who have received concurrent antitumor treatment or investigational products within 28 days or 5 half lives, whichever is shorter before the start of study intervention (e.g., chemotherapy, radiotherapy \[with the exception of palliative bone directed radiotherapy\], immunotherapy, targeted therapy, hormonal therapy, or cytokine therapy except for erythropoietin).
2. Participants who had major surgery within 28 days before the start of study intervention (excluding prior diagnostic biopsy).
3. Participants who had continuance of toxicities due to prior antitumor agents that have not resolved to Grade ≤ 1 per NCI CTCAE version 5.0, except alopecia, \< Grade 2 sensory neuropathy.
4. Participants with a history of immune mediated AE of any grade that resulted in discontinuation of prior immunotherapy.
5. Participants with previous malignant disease other than the target malignancy to be investigated in this study within the last 2 years with the exception of resected basal or squamous cell carcinoma of the skin, superficial bladder cancer, carcinoma in situ of the cervix or breast.
6. Participants with active leptomeningeal disease or uncontrolled, untreated brain metastasis. Participants with a history of treated and, at the time of screening, stable central nervous system (CNS) metastases are eligible, provided they meet all the following:
a. Brain imaging at screening shows no evidence of interim progression, participant is clinically stable for at least 2 weeks and without evidence of new brain metastases.
b. Measurable disease outside the CNS. c. No ongoing requirement for corticosteroids as therapy for CNS disease; off steroids 2 weeks before the first dose of AP203; anticonvulsants at a stable dose are allowed.
7. Participants who received any organ transplantation including allogeneic stem cell transplantation.
8. Participants with significant acute or chronic infections including, among others:
o Known history of testing positive test for human immunodeficiency virus (HIV) or known acquired immunodeficiency syndrome (AIDS).
Note: An HIV serology test (including antigen and/or antibodies) will be conducted at baseline for the participants with unknown HIV status and participants with positive HIV test will be excluded.
o Untreated chronic hepatitis B or chronic hepatitis B virus (HBV) carriers with HBV deoxyribonucleic acid (DNA) \> 500 IU/mL (or \> 2500 copies/mL) at screening.
Note: Inactive hepatitis B surface antigen (HBsAg) carriers, treated and stable hepatitis B (HBV DNA \< 500 IU/mL or \< 2500 copies/mL) can be enrolled. Participants with detectable HBsAg or detectable HBV DNA should be managed per treatment guidelines. Participants receiving antivirals at screening should have been treated for \> 2 weeks before the first dose of AP203.
o Participants with active hepatitis C. Note: Participants with a negative hepatitis C virus (HCV) antibody test at screening or positive HCV antibody test followed by a negative HCV ribonucleic acid (RNA) test at screening are eligible. The HCV RNA test will be performed only for participants testing positive for HCV antibody. Participants receiving antivirals at screening should have been treated for \> 2 weeks before the first dose of AP203.
9. Participants with active or history of any autoimmune disease that may relapse (participants with diabetes Type I, vitiligo, psoriasis, hypo- or hyperthyroid disease not requiring immunosuppressive treatment are eligible) or immunodeficiencies.
10. Participants with known severe hypersensitivity reactions to monoclonal antibodies.
11. Participants with pregnancy or lactation period. (Note: a negative pregnancy test is required for WOCBP.)
12. Participants with known alcohol or drug abuse.
13. Participants with clinically significant (i.e., active) cardiovascular disease: cerebral vascular accident/stroke (\< 6 months prior to the first dose of AP203), myocardial infarction (\< 6 months prior to the first dose of AP203), unstable angina, congestive heart failure (New York Heart Association Classification Class ≥ II), or serious uncontrolled cardiac arrhythmia requiring medication.
14. Participants with any psychiatric condition that would prohibit the understanding or rendering of informed consent.
15. Participants with live vaccination within 28 days of the first dose of AP203 and while on study is prohibited.
16. Participants with all other significant diseases, in the opinion of the Investigator, might impair the participant's tolerance of the study intervention.
* Dose expansion Phase specific Exclusion Criterion:
1. Participants who have received prior therapy with any PD-L1 x CD137 bispecific antibody.
