Simulations of magnetohydrodynamics convection in slowly rotating stars predict antisolar differential rotation (DR) in which the equator rotates slower than poles. This anti-solar DR in the usual αΩ dynamo model does not produce polarity reversal. Thus, the features of large-scale magnetic fields in slowly rotating stars are expected to be different than stars having solar-like DR. In this study, we perform mean-field kinematic dynamo modelling of different stars at different rotation periods. We consider anti-solar DR for the stars having rotation period larger than 30 days and solar-like DR otherwise. We show that with particular α profiles, the dynamo model produces magnetic cycles with polarity reversals even with the anti-solar DR provided, the DR is quenched when the toroidal field grows considerably high and there is a sufficiently strong α for the generation of toroidal field. Due to the anti-solar DR, the model produces an abrupt increase of magnetic field exactly when the DR profile is changed from solar-like to anti-solar. This enhancement of magnetic field is in good agreement with the stellar observational data as well as some global convection simulations. In the solar-like DR branch, with the decreasing rotation period, we find the magnetic field strength increases while the cycle period shortens. Both of these trends are in general agreement with observations. Our study provides additional support for the possible existence of anti-solar DR in slowly rotating stars and the presence of unusually enhanced magnetic fields and possibly cycles which are prone to production of superflare.