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The transverse injection painting scheme is widely adopted in many high-intensity hadron synchrotrons to alleviate space charge effects. As a common issue in such schemes, however, the utilization of the injection bump magnets during multiturn painting process can produce edge focusing effects, causing β-function beat and even beam loss. For instance, in the recently-built Rapid Cycling Synchrotron (RCS) of China Spallation Neutron Source (CSNS), the edge focusing effect of the dc injection bump magnets breaks the 4-fold symmetry of the RCS. In the upcoming upgrade project of the CSNS, the beam power is planned to increase to 500 kW. For such high-intensity circular accelerators operated with tunes above half-integer, the combined effect of the edge focusing and space charge becomes a key contribution to the beam loss, which should be subject to a strict control. To address this issue, the edge focusing effect of the injection bumps is analyzed via the model of coherent half-integer resonance, from which the stopband harmonics correction and β-beat correction method are proposed to minimize the emittance growth. To this end, 16 programmable trim quadrupoles are newly installed in the CSNS/RCS for the superperiodicity restoration. The experimental results show that the β-function is effectively compensated, the beam loss and the emittance growth are significantly reduced.