  Using the density functional theoretical calculations, we report a new set of
topological semimetals X$_{2}$YZ (X = \{Cu, Rh, Pd, Ag, Au, Hg\}, Y = \{Li, Na,
Sc, Zn, Y, Zr, Hf, La, Pr, Pm, Sm, Tb, Dy, Ho, Tm\} and Z =\{Mg, Al, Zn, Ga, Y,
Ag, Cd, In, Sn, Ta, Sm\}), which show the existence of multiple topological
triple point fermions along four independent $C_{3}$ axes. These fermionic
quasiparticles have no analogues elementary particle in the standard model. The
angle-resolved photoemission spectroscopy is simulated to obtain the exotic
topological surface states and the characteristic Fermi arcs. The inclusion of
spin-orbit coupling splits the triple-point into two Dirac points. The
triple-point fermions are exhibited on the easily cleavable (111) surface and
are well separated from the surface $\bar{\Gamma}$ point, allowing them to be
resolved in the surface spectroscopic techniques. This intermediate linearly
dispersive degeneracy between Weyl and Dirac points may offer prospective
candidates for quantum transport applications.
