  Using data samples collected with the BESIII detector operating at the BEPCII
storage ring, the cross section of the inclusive process $e^{+}e^{-} \to \eta +
X$, normalized by the total cross section of $e^{+}e^{-} \to \text{hadrons}$,
is measured at eight center-of-mass energy points from 2.0000 GeV to 3.6710
GeV. These are the first measurements with momentum dependence in this energy
region. Our measurement shows a significant discrepancy from calculations with
the existing fragmentation functions. To address this discrepancy, a new QCD
analysis is performed at the next-to-next-to-leading order with hadron mass
corrections and higher twist effects, which can explain both the established
high-energy data and our measurements reasonably well.
