  We present the first results from very-high-energy observations of the dwarf
spheroidal satellite candidate Triangulum II with the MAGIC telescopes from
62.4 hours of good-quality data taken between August 2016 and August 2017. We
find no gamma-ray excess in the direction of Triangulum II, and upper limits on
both the differential and integral gamma-ray flux are presented. Currently, the
kinematics of Triangulum II are affected by large uncertainties leading to a
bias in the determination of the properties of its dark matter halo. Using a
scaling relation between the annihilation J-factor and heliocentric distance of
well-known dwarf spheroidal galaxies, we estimate an annihilation J-factor for
Triangulum II for WIMP dark matter of $\log[J_{\text{ann}}({0.5^{\circ}})/$
GeV$^{2}$ cm$^{-5}] = 19.35 \pm 0.37$. We also derive a dark matter density
profile for the object relying on results from resolved simulations of Milky
Way sized dark matter halos. We obtain 95% confidence-level limits on the
thermally averaged annihilation cross section for WIMP annihilation into
various Standard Model channels. The most stringent limits are obtained in the
$\tau^{+}\tau^{-}$ final state, where a cross section for annihilation down to
$\langle \sigma_{\text{ann}} v \rangle = 3.05 \times 10^{-24}$ cm$^{3}$
s$^{-1}$ is excluded.
