  A thin, narrow-bandgap semiconductor Bi$_2$O$_2$Te nanosheet is obtained via
mechanical exfoliation and a Hall-bar device is fabricated from it on a heavily
doped Si/SiO$_2$ substrate and studied at low temperatures. Gate transfer
characteristic measurements show that the transport carriers in the nanosheet
are of $n$-type. The carrier density, mobility, and mean free path in the
nanosheet are determined by measurements of the Hall resistance and the
longitudinal resistance of the Hall-bar device and it is found that the
electron transport in the nanosheet is in a quasi-two-dimensional (2D),
strongly disordered regime. Magnetotransport measurements for the device at
magnetic fields applied perpendicular to the nanosheet plane show dominantly
weak antilocalization (WAL) characteristics at low fields and a linear
magnetoresistance (LMR) behavior at large fields. We attribute the WAL
characteristics to strong spin-orbit interaction (SOI) and the LMR to the
classical origin of strong disorder in the nanosheet. Low-field
magnetoconductivity measurements are also performed and are analyzed based on
the multi-channel Hikami-Larkin-Nagaoka theory with the LMR correction being
taken into account. The phase coherence length, spin relaxation length,
effective 2D conduction channel number and coefficient in the linear term due
to the LMR in the nanosheet are extracted. It is found that the spin relaxation
length in the Bi$_2$O$_2$Te nanosheet is several times smaller than it in its
counterpart Bi$_2$O$_2$Se nanosheet and thus an ultra-strong SOI is present in
the Bi$_2$O$_2$Te nanosheet. Our results reported in this study would greatly
encourage further studies and applications of this emerging narrow-bandgap
semiconductor 2D material.
