We report on the magnetization and anomalous Hall effect (AHE) in the high-quality single crystals of the kagome magnet YbMn$_{6}$Sn$_{6}$, where the spins of the Mn atoms in the kagome lattice order ferromagnetically and the intermediate-valence Yb atoms are nonmagnetic. The intrinsic mechanism plays a crucial role in the AHE, leading to an enhanced anomalous Hall conductivity (AHC) compared with the other rare-earth $R$Mn$_{6}$Sn$_{6}$ compounds. Our band structure calculation reveals a strong hybridization between the 4f electrons of Yb and conduction electrons.

We report the physical properties of ThRu$_3$Si$_2$ featured with distorted Ru kagome lattice. The combined experiments of resistivity, magnetization and specific heat reveal bulk superconductivity with $T_{\rm{c}}= 3.8$ K. The specific heat jump and calculated electron-phonon coupling indicate a moderate coupled BCS superconductor. In comparison with LaRu$_3$Si$_2$, the calculated electronic structure in ThRu$_3$Si$_2$ shows an electron-doping effect with electron filling lifted from 100 meV below flat bands to 300 meV above it. This explains the lower superconducting transition temperature and weaker electron correlations observed in ThRu$_3$Si$_2$. Our work suggests the $T_{\rm{c}}$ and electronic correlations in the kagome superconductor could have an intimate connection with the flat bands.

The kagome superconductor CsV$_{3}$Sb$_{5}$ has attracted widespread attention due to its rich correlated electron states including superconductivity, charge density wave (CDW), nematicity, and pair density wave. Notably, the modulation of the intertwined electronic orders by the chemical doping is significant to illuminate the cooperation/competition between multiple phases in kagome superconductors. In this study, we have synthesized a series of tantalum-substituted Cs(V$_{1-x}$Ta$_{x}$)$_{3}$Sb$_{5}$ by a modified self-flux method. Electrical transport measurements reveal that CDW is suppressed gradually and becomes undetectable as the doping content of $ x$ is over 0.07. Concurrently, the superconductivity is enhanced monotonically from $T_{\rm c} \sim 2.8 $ K at $x =0$ to 5.2 K at $x = 0.12$. Intriguingly, in the absence of CDW, Cs(V$_{1-x}$Ta$_{x}$)$_{3}$Sb$_{5}$ ($x = 0.12$) crystals exhibit a pronounced two-fold symmetry of the in-plane angular-dependent magnetoresistance (AMR) in the superconducting state, indicating the anisotropic superconducting properties in the Cs(V$_{1-x}$Ta$_{x}$)$_{3}$Sb$_{5}$. Our findings demonstrate that Cs(V$_{1-x}$Ta$_{x}$)$_{3}$Sb$_{5}$ with the non-trivial band topology is an excellent platform to explore the superconductivity mechanism and intertwined electronic orders in quantum materials.