  Unconventional fermions, such as three-fold, four-fold, six-fold, and
eight-fold fermions have attracted intense attention in recent years. However,
the concrete materials hosting unconventional fermions are still in urgent
scarcity. In this work, based first-principle calculations and symmetry
analysis, we reveal rich unconventional fermions in existing compound Re2C3 (Re
= Y, La, Ce, Pr, Nd, Sm, Tb, Dy, Ho, Er, Tm, Yb, Lu). We show that these
compounds host quadratic dispersive three-fold (TP), linear dispersive
four-fold (FP) and six-fold points (SP) near the Fermi level in their electric
band structures when spin-orbital coupling (SOC) is not included. Notably, the
FP is charge-2 Dirac-like point. More importantly, among compound Re2C3, the
compound Yb2C3 has very clean band structure, and its unconventional fermions
are closed to the Fermi level. We also find that a uniaxial strain can
transform the unconventional fermions into other types fermions, depending on
the directions of strain. When SOC is considered, a SP transform to an
eightfold degenerate point and a fourfold degenerate point. Overall, our work
provides a family of realistic materials to study the unconventional fermions.
