In a multicarrier NOMA system, the subchannel allocation (SA) and power allocation (PA) are intricately linked and essential for improving system throughput. Also, for the successful execution of successive interference cancellations (SIC) at the receiver, a minimum power gap is required among users. As a result, this research comes up with optimization of the SA and PA to maximize the sum rate of the NOMA system while sticking to the minimum power gap constraint in addition to minimum user rate, maximum number of users in a subchannel and power budget constraints for downlink transmission in multicarrier NOMA networks. To ensure that the formulated problem can be solved in polynomial time, we propose solving it in two stages; SA followed by PA. To obtain SA, we investigate four algorithms: Greedy, WSA, WCA, and WCF. For PA, we propose a low-complexity algorithm. We compare the performance of the proposed method with benchmark method that does not consider the minimum power gap constraint. We conclude that employing WCF algorithm with the PA algorithm gives the best sum rate performance.