Abstract After the discovery of topological insulators (TIs), it has come to be widely recognized that topological states of matter can actually be widespread. In this sense, TIs have established a new paradigm about topological materials. Recent years have seen a surge of interest in topological semimetals, which embody two different ways of generalizing the effectively massless electrons to bulk materials. Dirac and, particularly, Weyl semimetals should support several transport and optical phenomena that are still being sought in experiments. A number of promising experimental results indicate superconductivity in members of half-Hesuler semimetals which realize the mixing singlet and triplet pairing symmetry. We now turn to results we got through the work on topological semimetals. This work presents quantum high field transports on Dirac and Weyl topological semimetals including Sr1-yMn1-zSb2 (y, z < 0.1), YbMnBi2 and TaP. In case of Sr1-yMn1-zSb2 (y, z < 0.1), massless relativistic fermion was reported with m* = 0.04-0.05m0. This material presented a ferromagnetic order for in 304 K < T < 565 K, but a canted antiferromagnetic order with a net ferromagnetic component for T < 304 K. These are considered striking features of Dirac fermions For YbMnBi2, we reported the unusual interlayer quantum transport behavior in magnetoresistivity, resulting from the zeroth LL mode observed in this time reversal symmetry breaking type II Weyl semimetal. Also, for Weyl semimetal TaP the measurements probed multiple Fermi pockets, from which nontrivial π Berry phase and Zeeman splitting were extracted. Our ultra-low penetration depth measurements on half-Heuslers YPdBi and TbPdBi revealed a power- law behavior with n= 2.76 ± 0.04 for YPdBi samples and n=2.6 ± 0.3 for TbPdBi sample. We may conclude the exponent n > 2 implies nodless superconducting gap in our samples. Also, we found that despite the increase in magnetic correlations from YPdBi to TbPdBi, superconductivity remains robust in both systems which indicates that AF fluctuations do not play a major role in superconducting mechanism.