This paper develops a strategy-proof and Pareto efficient mechanism for a school choice program called Top Trading Cycles among Representatives with Supplementary Seats (TTCR-SS). We consider a setting where minimum quotas are imposed for each school, i.e., a school is required to be assigned at least a certain number of students to operate, and the obtained matching must respect initial endowments, i.e., each student must be assigned to a school that is at least as good as her initial endowment school. Although minimum quotas are relevant in school choice programs and strategy-proofness is important to many policymakers, few existing mechanisms achieve both of them simultaneously. Furthermore, existing mechanisms require that all students consider all schools acceptable to obtain a feasible matching that respects minimum quotas and cannot guarantee Pareto efficiency. TTCR-SS is based on Top Trading Cycles (TTC) mechanism, while it is significantly extended to handle the supplementary seats of schools while respecting minimum quotas. Our simulation results show TTCR-SS is significantly better than an existing TTC-based mechanism in terms of students' welfare.