  Sunspot chromospheres display vigorous oscillatory signature when observed in
chromospheric diagnostics like the strong Ca II lines and H-alpha. New
high-resolution sunspot observations from the Swedish 1-m Solar Telescope show
the ubiquitous presence of small-scale periodic jet-like features that move up
and down. This phenomenon has not been described before. Their typical width is
about 0.3 arcsec and they display clear parabolic trajectories in space-time
diagrams. The maximum extension of the top of the jets is lowest in the umbra,
a few 100 km, and progressively longer further away from the umbra in the
penumbra, with the longest more than 1000 km. These jets resemble dynamic
fibrils found in plage regions but at smaller extensions. LTE inversion of
spectro-polarimetric Ca II 8542 observations enabled for a comparison of the
magnetic field inclination and the properties of these short jets. We find that
the most extended of these jets also have longer periods and tend to be located
in regions with more horizontal magnetic fields. This is a direct observational
confirmation of the mechanism of long-period waves propagating along inclined
magnetic fields into the solar chromosphere. This mechanism was identified
earlier as the driver of dynamic fibrils in plage, part of the mottles in quiet
Sun, and type I spicules at the limb. The sunspot dynamic fibrils that we
report here represent a new class of manifestation of this mechanism. They are
not the same as the transient penumbral and umbral micro-jets reported earlier.
