  Simulations of magnetohydrodynamics convection in slowly rotating stars
predict anti-solar differential rotation (DR) in which the equator rotates
slower than poles. This anti-solar DR in the usual $\alpha \Omega$ 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 $\alpha$ 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 $\alpha$ 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.
