Exotic massless fermionic excitations with non-zero Berry flux, other than Dirac and Weyl fermions, could exist in condensed matter systems under the protection of crystalline symmetries, such as spin-1 excitations with 3-fold degeneracy and spin-3/2 Rarita-Schwinger-Weyl fermions. Herein, by using ab initio density functional theory, we show that these unconventional quasiparticles coexist with type-I and type-II Weyl fermions in a family of transition metal silicides, including CoSi, RhSi, RhGe and CoGe, when the spin-orbit coupling (SOC) is considered. Their non-trivial topology results in a series of extensive Fermi arcs connecting projections of these bulk excitations on side surface, which is confirmed by (010) surface electronic spectra of CoSi. In addition, these stable arc states exist within a wide energy window around the Fermi level, which makes them readily accessible in angle-resolved photoemission spectroscopy measurements.Introduction.-Three types of fermions play fundamental roles in our understanding of nature: Majorana, Dirac and Weyl [1]. Much attention has been paid to looking for these fundamental particles in high energy physics during past few decades, whereas only signature of Dirac fermions is captured. Interestingly, the same movement comes up in the field of condensed matter physics [2], and great achievements have been made in last few years. For example, the Majorana-like excitations are detected in superconducting heterostructures [3][4][5][6]; the Dirac [7][8][9][10][11][12] and Weyl [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29] fermions are observed in some compounds. These quasiparticles in solid states are not only important for basic science, but also show great potential for practical applications on new devices [30,31].Because symmetries in condensed matter physics are usually much lower than the Poincaré symmetry in high energy physics, quasiparticles in solid states are less constrained such that various new types of fermionic excitations are predicted to exist in 3D lattices [32]. Among these allowed by space group (SG) symmetries are spin-1 and spin-3/2 massless fermionic excitations, besides the well-known spin-1/2 case, namely the Weyl fermion. All of these massless quasiparticles can be described by the low energy Hamiltonian in a unified manner to the linear order of momentum