Applying angle-resolved photoemission spectroscopy and density functional theory calculations, we present compelling spectroscopic evidence demonstrating the intertwining and mutual interaction between the Kondo and kagome sublattices in heavy-fermion intermetallic compound YbV_{6}Sn_{6}. We reveal the Yb 4f-derived states near the Fermi level, along with the presence of bulk kagome bands and topological surface states. We unveil strong interactions between the 4f and itinerant electrons, where the kagome bands hosting the Dirac fermions and van Hove singularities predominate. Such findings are well described using a c-f hybridization model. On the other hand, our systematic characterization of magnetic properties demonstrates an unusually enhanced antiferromagnetic ordering, where the kagome-derived van Hove singularities near E_{F} play a vital role in determining the unconventional nature of the Ruderman-Kittel-Kasuya-Yosida interaction and Kondo coupling. These unique kagome-state-mediated exchange interactions have never been reported before and could lead to a novel phase diagram and various quantum critical behaviors in YbV_{6}Sn_{6} and its siblings. Our results not only expand the family of exotic quantum phases entangled with kagome structure to the strongly correlated regime, but also establish YbV_{6}Sn_{6} as an unprecedented platform to explore unconventional many-body physics beyond the standard Kondo picture.