Recall the glycosidic linkages in common disaccharides/polysaccharides

• Lactose is composed of $\beta$-D-galactose and D-glucose joined by a $\beta(1\to 4)$ glycosidic bond.
• Sucrose has glucose and fructose joined by an $\alpha(1\to 2)\beta$ linkage.
• Maltose consists of two glucose units joined by an $\alpha(1\to 4)$ linkage.
• Amylose is a polymer of glucose having $\alpha(1\to 4)$ glycosidic linkages.

Match with the required linkage

The question asks for a compound containing $\beta$-$C_1-C_4$ glycosidic linkage, i.e. $\beta(1\to 4)$ linkage.

Check each option

• A: Lactose $\rightarrow \beta(1\to 4)$ ✅
• B: Sucrose $\rightarrow \alpha(1\to 2)\beta$ ❌
• C: Maltose $\rightarrow \alpha(1\to 4)$ ❌
• D: Amylose $\rightarrow \alpha(1\to 4)$ ❌

Conclusion

The compound containing $\beta$-$C_1-C_4$ glycosidic linkage is lactose.