This is the first study to consider a quantum dot with screw dislocation that has Rosen-Morse (RM) confinement potential, generated by a GaAs/GaAlAs heterostructure. An external magnetic field and Aharonov-Bohm (AB) flux field were also applied on RM quantum dot (RMQD) in order to stave the effects of a screw dislocation defect. The combined effect of the screw dislocation defect, the external magnetic field, and AB flux field on the total refractive index changes (TRICs) and the total absorption coefficients (TACs) of RMQD are thus investigated. Cylindrical coordinates are used due to the direction of application of the torsion and the external fields, as well as due to the structure's symmetry. The effective mass approximation and tridiagonal matrix methods are used in order to obtain the subband energy spectra and electronic wave functions of RMQD. The nonlinear optical specifications of RMQD are checked using compact-density-matrix formalism within the framework of the iterative method. Reviews without screw dislocation are also carried out in order to be able to clarify the effects of a screw dislocation defect on the optical properties, and then, both cases are deliberated. This study is the first attempt to analyze the AB flux field for RMQD without screw dislocation. In the present study, the influences of a screw dislocation defect on RMQD's TRICs and TACs are probed by considering different values of the external magnetic field and AB flux field, and the ranges of corresponding parameters on the optimum of the structure are specified. Moreover, the study also elucidates how to rule out the effects of screw dislocation on optical specifications by means of the external fields. Despite a certain screw dislocation, the frequency range is determined where the structure behaves as if it is perfect (namely, without screw dislocation) for its optimum, which in turn is crucial for experimental applications.