This thesis summarizes our eorts to develop and explore potential routes for the discovery of new superconductors. The development of viable solutions for sulfur-bearing compounds is presented. It also provides the details of searching for quantum critical points (QCPs) and possible superconductors by suppressing ferromagnetic states via chemical substitution and the application of pressure. The ferromagnetism in La(V_{>xCr1-x)Ge3 was successfully suppressed}

by pressure, and, in addition, a potential QCP at ambient pressure was discovered for x=0.16. On the other hand, the La(V_{xCr1-x)Sb3 series is likely to evolve into new magnetic state with V-substitution with the Cr-based magnetism appearing to be more local-moment like than for the case of LaCrGe3. We also performed detailed characterization on BaSn5 superconductor, giving further understanding of its superconducting state, and on R3Ni2-xSn7 and RNi1-xBi2y series putting to rest spurious claims of superconductivity.}