Confined water has demonstrated distinct structural and dynamic properties compared to bulk water. Although many studies have explored the water structure within simple geometries using materials such as carbon and silica, studies on gas solubility in confined water and the underlying physics of water structure-solubility remain limited. Recent research has illuminated the concept of "oversolubility", wherein gases display increased solubility within liquids confined in small pores compared to their bulk form. This study focuses on zeolites, naturally abundant materials with versatile applications, to study the hydrogen solubility within confined water through careful experimentation. Our findings underscore the relationship between the pore dimension and gas solubility enhancement within confined water. Hydrogen solubility is closely associated with the rearrangement of water molecules within the porous framework of the zeolite. Our research shows that a 2 nm pore size results in the greatest increase in hydrogen solubility in the water trapped inside the zeolite framework. The double donor-double acceptor (DDAA) bonds play a critical role in hydrogen solubility. Our research provides fundamental insight into the role of the molecular bonding type on hydrogen solubility in water, paving the way for potential applications in hydrogen storage and utilization.