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The role of the triangle mechanism in the decay process B0→J/ψ K0f0→J/ψ K0π+π- and B0 J/ψ K0a0→J/ψ K0 π0η is probed. In these process, the triangle singularity appears from the decay of B0 into J/ψΦK0 then Φ decays into K0barK0 and K0barK0 merged intof0 or a0 which finally decay into π+π- and π0η respectively. We find that this mechanism leads to a triangle singularity around Minv(K0f0(a0))≈1520 MeV, and gives sizable branching fractions Br(B0→J/ψ K0f0→J/ψ K0π+π-)=7.67×10-7 and Br(B0→J/ψ K0a0→ J/ψ K0 π0η)=1.42×10-7. This potential investigation can help us obtain the information of the scalar meson f0(980) or a0(980). Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Article funded by SCOAP3 and published under licence by Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy of Science and the Institute of Modern Physics of the Chinese Academy of Sciences and IOP Publishing Ltd.