  The Curie constants $C^{*} = \lim_{T\rightarrow 0}T\chi_{\text{imp}}$ of a
spin-1/2 and a spin-1 impurities are calculated using the quantum Monte Carlo
simulations. Here the impurity susceptibility $\chi_{\text{imp}}$ is the
difference between the uniform susceptibilities with and without the impurity
and $T$ is the temperature. Moreover, the two-dimensional quantum $JQ_3$ model
on the honeycomb lattice is considered as the host system. $T\chi_{\text{imp}}$
as a function $T$ is investigated in great detail. Remarkably, our data
indicate strongly that $C^* > 0.25$ and $C^* > 2/3$ for the spin-1/2 and the
spin-1 impurities, respectively. In particular, although no definite conclusion
is obtained due to finite-size effects, we find the Curie constant associated
with a spin-1/2 impurity likely converges to a value greater than the
established result of 0.262(2) in the literature. The outcomes reached here
provide certain evidence that fractional impurity spin is observed for the
studied $JQ_3$ system.
