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Two-dimensional (2D) metal-organic frameworks (MOFs) offer opportunities for physical property adjustments in heterostructures based on various substrates. While 2D MOFs on metallic surfaces have been widely reported, combinations of MOFs and 2D or quasi 2D emergent crystals are rare but full of potential. Using scanning tunneling microscopy (STM) and spectroscopy (STS) at a low temperature, we investigated in-situ grown PTCDA (perylene-3,4,9,10-tetracarboxylic dianhydride)-based monolayer sheets on the surface of Fe-intercalated TaS₂ (Fe_0.24TaS₂). Depending on post-annealing temperatures, PTCDA molecules form a self-assembly monolayer and different types of Fe-PTCDA frameworks with residual Fe atoms on the Fe_0.24TaS₂ surface. Annealed at a high temperature, a stable honeycomb MOF appears, of which the detailed structure was resolved. STS results unveil the shifting of the PTCDA Fermi level in different MOFs. Our work exhibits controllable interfacial electronic structures between PTCDA and Fe_0.24TaS₂, and suggests fabrications of organic heterostructures on quasi 2D emergent crystals.