  Fractionalization of quantum degrees of freedom holds the key to finding new
phenomena in physics, e.g., the quark model in hadron physics, the spin-charge
separation in strongly-correlated electron systems, and the fractional quantum
Hall effect. A typical example of the fractionalization in quantum spin systems
is the spin-$1$ Haldane state, whose intriguing characteristics are well
described by fractionalized $S=1/2$ virtual spins in a bilinear-biquadratic
spin-$1$ chain, the so-called Affleck--Kennedy--Lieb--Tasaki model, delivering
two individual spin-$1/2$ degrees of freedom as edge states. Here we
theoretically propose an exotic extension of the Haldane state and chirality in
a triangular spin tube, inducing a quasi-fractionalization of spin-$1/2$ degree
of freedom, i.e., a quarter spin. Existence of the edge state is confirmed both
analytically and numerically, combining a low-energy perturbation theory and
variational matrix-product state method. Our study can not only propose a new
quantum spin property but pave a way to novel quantum states of matter.
