Small molecules with nitrogen-containing scaffolds have gained much attention due to their biological importance in the development of new anticancer agents. The present paper reports the synthesis of a library of new dihydropyridine and pyridine analogs with diverse pharmacophores. All compounds were tested against the human tissue nonspecific alkaline phosphatase (h-TNAP) enzyme. Most of the compounds showed excellent enzyme inhibition against h-TNAP, having IC50 values ranging from 0.49 ± 0.025 to 8.8 ± 0.53 µM, which is multi-fold higher than that of the standard inhibitor (levamisole = 22.65 ± 1.60 µM) of the h-TNAP enzyme. Furthermore, an MTT assay was carried out to evaluate cytotoxicity against the HeLa and MCF-7 cancer cell lines. Among the analogs, the most potent dihydropyridine-based compound 4d was selected to investigate pro-apoptotic behavior. The further analysis demonstrated that compound 4d played a significant role in inducing apoptosis through multiple mechanisms, including overproduction of reactive oxygen species, mitochondrial dysfunction, DNA damaging, and arrest of the cell cycle at the G1 phase by inhibiting CDK4/6. The apoptosis-inducing effect of compound 4d was studied through staining agents, microscopic, and flow cytometry techniques. Detailed structure–activity relationship (SAR) and molecular docking studies were carried out to identify the core structural features responsible for inhibiting the enzymatic activity of the h-TNAP enzyme. Moreover, fluorescence emission studies corroborated the binding interaction of compound 4d with DNA through a fluorescence titration experiment.