The present study deals with the advanced in-silico analyses of several Apigenin derivatives to explore human papillomavirus-associated cervical cancer and DNA polymerase theta inhibitor properties by molecular docking, molecular dynamics, QSAR, drug-likeness, PCA, a dynamic cross-correlation matrix and quantum calculation properties. The initial literature study revealed the potent antimicrobial and anticancer properties of Apigenin, prompting the selection of its potential derivatives to investigate their abilities as inhibitors of human papillomavirus-associated cervical cancer and DNA polymerase theta. In silico molecular docking was employed to streamline the findings, revealing promising energy-binding interactions between all Apigenin derivatives and the targeted proteins. Notably, Apigenin 4′-O-Rhamnoside and Apigenin-4′-Alpha-L-Rhamnoside demonstrated higher potency against the HPV45 oncoprotein E7 (PDB ID 2EWL), while Apigenin and Apigenin 5-O-Beta-D-Glucopyranoside exhibited significant binding energy against the L1 protein in humans. Similarly, a binding affinity range of − 7.5 kcal/mol to − 8.8 kcal/mol was achieved against DNA polymerase theta, indicating the potential of Apigenin derivatives to inhibit this enzyme (PDB ID 8E23). This finding was further validated through molecular dynamic simulation for 100 ns, analyzing parameters such as RMSD, RMSF, SASA, H-bond, and RoG profiles. The results demonstrated the stability of the selected compounds during the simulation. After passing the stability testing, the compounds underwent screening for ADMET, pharmacokinetics, and drug-likeness properties, fulfilling all the necessary criteria. QSAR, PCA, dynamic cross-correlation matrix, and quantum calculations were conducted, yielding satisfactory outcomes. Since this study utilized in silico computational approaches and obtained outstanding results, further validation is crucial. Therefore, additional wet-lab experiments should be conducted under in vivo and in vitro conditions to confirm the findings.