The interchange-like transport is observed between two resonant surfaces (q = 1 and q = 4/3, where q is the safety factor) in a finite small positive magnetic shear regime with mild core oscillations in the experimental advanced superconducting tokamak strong on-axis electron heating H-mode plasmas. It is synchronized with the increasing gradient of the soft X-ray profile and the intensifying electron density fluctuations in the core. The analysis of two-fluid simulations combined with experimental measurements indicates the destabilization of collective resistive interchange modes with several toroidal mode numbers. The overall effect of modes leads to strong perturbations at the two resonant surfaces in contrast to that between them where the anomalous electron flux is low. Their radial displacement is beyond the resistive layer width which satisfies the condition for the nonlinear destabilization of tearing modes [L. Comisso et al., Phys. Plasmas 23, 100702 (2016)]. Evidence and analysis shown in this paper tend to understand the mechanism of mild oscillations in the core.