Step 1: Understanding the Question:
The problem asks for the specific type of glycosidic linkage that connects the monosaccharide units together to form the disaccharide lactose (commonly known as milk sugar).
Step 2: Detailed Explanation:
Lactose is a disaccharide sugar composed of two distinct monosaccharide subunits: $\beta$-D-galactose and $\beta$-D-glucose.
The condensation reaction occurs between the anomeric carbon C1 of the $\beta$-D-galactose molecule and the hydroxyl (-OH) group on the C4 position of the $\beta$-D-glucose molecule.
Because the hemiacetal hydroxyl group at C1 of galactose points upwards in the $\beta$ configuration, the resulting oxide bridge holding the two rings together is classified as a $\beta$-1,4-glycosidic linkage.
Looking at other options, an $\alpha$-1,4-linkage is found in maltose, $\alpha$-1,6-linkages form the branches in amylopectin, and $\alpha,\beta$-1,2-linkages connect sucrose.
Step 3: Final Answer:
The glycosidic bond present inside lactose is a $\beta$-1,4-glycosidic linkage, which corresponds to option (C).