Recent analysis of nucleosynthetic isotopes in meteorites show that the meteorites can be classified as Non-carbonaceous (NC) meteorites and Carbonaceous (CC) meteorites. The isotopic dichotomy suggests that there was a mechanism that maintained the spatial heterogeneous isotopic distribution in the solar nebula. A potential scenario for the origin of the isotopic heterogeneity is the early Jupiter scenario. Because the massive planets can create gas gaps in protoplanetary disks, the gap created by the early Jupiter can filter dust aggregates drifting from outside Jupiter into inside Jupiter. Thus, early Jupiter can divide the protoplanetary disks spatially into the dust reservoir inside Jupiter (NC reservoir) and the dust reservoir outside Jupiter (CC reservoir). However, the tiny fragments formed by dust collisions at the CC reservoir can leak into the NC reservoir via turbulent diffusion. Therefore, it is important for the early Jupiter scenario to reveal how the leakage of tiny dust aggregates affects isotopic ratios at the two reservoirs. We construct a model to simulate the evolution of the dust size distribution and an isotopic ratio in protoplanetary disks with a planetary gap. We simulate the evolution of the dust size and 54Cr isotopic ratio (ε54Cr) with heterogeneous Cr isotope distribution. Assuming the position of two NC and CC reservoirs, we survey the time evolution of ε54Cr at the two reservoirs. Our results show that ε54Cr value at the NC reservoir is different from the one at the CC reservoir in both cases with and without dust leaking. We also found that the weak filtering of the dust fragments increases ε54Cr at the NC reservoir for several Myrs. The time variation of ε54Cr at the NC reservoir by the weak filtering is consistent with the correlation between ε54Cr and the accretion ages of NC meteorites.