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A non-monotonic behavior of the velocity gradient of a test particlerevolving around a rapidly rotating black hole in the locally non-rotatingframe of reference is known as the Aschenbach effect. This effect can serve asa distinguishing signature of rapidly rotating black holes, being potentiallyuseful for the measurements of the astrophysical black hole spins. This paperis the generalization of our previous research to the motion of spinningparticles around a rotating black hole with non-zero cosmological constant. Weshow that both the particle's spin $s$ and the cosmological constant $\Lambda$modify the critical value of the black hole spin $a_c$, for which theAschenbach effect can be observed; $a_c$ can increase or decrease depending onthe signs of $s$ and $\Lambda$. We also found that the particle's spin $s$ canmimic the effect of the cosmological constant $\Lambda$ for a given $a_c$,causing thus a discrepancy in the measurements of $s$, $\Lambda$ and $a_c$ inthe Aschenbach effect.

Aschenbach effect for spinning particles in Kerr-(A)dS spacetime