Step 1: Concept Cation exchange resins are high molecular weight, cross-linked polymers containing acidic functional groups.
Step 2: Meaning These resins exchange their $H^{+}$ ions for cations like $Ca^{2+}$ or $Mg^{2+}$ present in hard water.
Step 3: Analysis Strong acid cation resins typically contain sulfonic acid groups (-$SO_{3}H$), while weak acid ones might contain carboxylic groups (-COOH).
Step 4: Conclusion Among the options, -$SO_{3}H$ is the standard functional group for cation exchange.
Final Answer: (B)