The angular-dependent magnetoresistance (AMR) of the ab plane is measured on the single crystals of iron-chalcogenide FeSe1βx
S
x
(x = 0, 0.07, 0.13 and 1) and FeSe1βy
Te
y
(y = 0.06, 0.61 and 1) at various temperatures under fields up to 9 T. A pronounced twofold-anisotropic carrier-scattering effect is identified by AMR, and attributed to a magnetic-field-induced spin nematicity that emerges from the tetragonal normal-state regime below a characteristic temperature T
sn. This magnetically polarized spin nematicity is found to be ubiquitous in the isoelectronic FeSe1βx
S
x
and FeSe1βy
Te
y
systems, no matter whether the sample shows an electronic nematic order at T
s β² T
sn, or an antiferromagnetic order at T
N < T
sn, or neither order. Importantly, we find that the induced spin nematicity shows a very different response to sulfur substitution from the spontaneous electronic nematicity: The spin-nematic T
sn is not suppressed but even enhanced by the substitution, whereas the electronic-nematic T
s is rapidly suppressed, in the FeSe1βx
S
x
system. Furthermore, we find that the superconductivity is significantly suppressed with the enhancement of the induced spin nematicity in both FeSe1βx
S
x
and FeSe1βy
Te
y
samples.