Inclusion Criteria:
* ≥ 18 years of age on day of signing informed consent
* histologically or cytologically confirmed diagnosis of cutaneous, subcutaneous, soft tissue, or nodal advanced solid tumor malignancy; metastatic disease eligible
* measurable disease per RECIST v1.1 - Note: Must have at least 1 tumor lesion with longest dimension of ≥ 10 mm (≥ 15 mm for the short axis for malignant lymph node lesions) that - For Part 1 only: can be easily palpated or detected by ultrasound to facilitate IT injection of ANK-101 (i.e., tumor in skin, muscle, subcutaneous tissue, or accessible lymph node) or; - For Part 2 only: can be accessed by interventional radiologic or endoscopic procedures for injection (e.g., ultrasound or computed tomography \[CT\] guided). - For Part 2 Dose Expansion Cohort only: Histologically confirmed Stage III or Stage IV NSCLC
* Part 3 CSCC Combination Cohort: Histologically confirmed high-risk locally advanced or metastatic CSCC not amenable to surgical management as determined by a multidisciplinary tumor board.
* documented disease progression, be refractory to, or intolerant of existing SOC therapy(ies) known to provide clinical benefit (including surgical cure) or not be eligible for SOC therapy(ies)
* ECOG performance status 0-1
* life expectancy \> 12 weeks
* adequate bone marrow, hepatic and renal function
* baseline electrocardiogram (EKG) without evidence of acute ischemia or prolonged QTc interval \> 460 msec
* Human immunodeficiency virus (HIV) infected participants must be on anti-retroviral therapy (ART) and have well-controlled HIV infection/disease
* last dose of previous anticancer therapy (including investigational agents) ≥ 28 days, radiotherapy ≥ 14 days (targeted palliative radiotherapy is allowed for lesions not planned for injections), or surgical intervention ≥ 21 days prior to the start of treatment
* resolution of all prior anticancer therapy toxicities (except for alopecia or vitiligo) to ≤ Grade 1 (as per NCI CTCAE Version 5.0)
* willing to provide pre- and post-treatment tumor biopsy samples if medically feasible
* participant is capable of understanding and complying with protocol requirements
Exclusion Criteria:
* injectable tumors impinging upon major airways or blood vessels
* prior treatment with recombinant interleukin-12 (IL-12)
* have received systemic therapy with immunosuppressive agents ≤ 28 days before the start of treatment
* have received live vaccines within 28 days prior to the start of ANK-101 treatment
* have primary or acquired immunodeficient states (e.g., leukemia, lymphoma)
* a woman of childbearing potential (WOCBP) who has a positive serum pregnancy test (within 72 hours) prior to the start of treatment or female participant who is breastfeeding
* prior organ transplantation
* known history of hepatitis B virus, known active hepatitis C virus, or a positive serological test at screening within 28 days prior to the start of treatment
* HIV-infected participants with a history of Kaposi sarcoma and/or Multicentric Castleman Disease
* active autoimmune disease or medical conditions requiring chronic steroid (i.e., ≥ 20 mg/day prednisone or equivalent) or other immunosuppressive therapy within 28 days prior to the start of treatment
* known active central nervous system (CNS) metastases
* congestive heart failure (\> New York Heart Association Class II), active coronary artery disease, unevaluated new onset angina within 3 months or unstable angina (angina symptoms at rest), or clinically significant cardiac arrhythmias
* uncontrolled bleeding disorders within 4 weeks prior to the start of treatment or known bleeding diathesis - Note: Part 2 only: Participants with active bleeding diathesis or requirement for therapeutic anticoagulation that cannot be interrupted or altered for procedures
* history of hypersensitivity to compounds of similar biological composition to IL-12, aluminum hydroxide, or drugs formulated with polysorbate-20
* other systemic conditions or organ abnormalities that, in the opinion of the Investigator, may interfere with the conduct and/or interpretation of the current study
* any acute or chronic psychiatric problems or substance abuse disorder that, in the opinion of the Investigator, make the participant unsuitable for participation
* Part 3 only: prior Grade 3 or greater immune-mediated adverse events (imAEs) following treatment with an agent that blocks the programmed cell death protein 1 (PD-1)/programmed cell death ligand 1 (PD-L1) pathway.
* Part 3 only: hypersensitivity to cemiplimab or any of its excipients or contraindications to cemiplimab per approved local labeling
