Type III Superconductivity Theory is an exploratory supplement to Type I and Type II Superconductivity Theory.
Paper link: https://arxiv.org/abs/2303.14673
In this theory, the authors claim that Type III Superconductivity can't have true Meissner effect.
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In type III superconductors Hc1 = 0 and vortices, which, as mentioned above, in this case do not possess normal core, can penetrate at any magnetic field (corresponding to a flux at least equal to a quantum flux), and there is no true Meissner state.
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P.S. This paper was already published as early as March this year, so it doesn't have a direct relationship with the current hot topic of Room-Temperature Ambient-Pressure Superconductor LK-99.
Well, to your possible concern, I think this bet will get "Yes" if the specific Paper "Type III superconductivity"(https://arxiv.org/abs/2303.14673) is widely accepted by other scientists and papers, especially we can find it easily in wiki "Superconductivity" like Type I & II. And in other situations, it will be "No".