  Solar jets are well-collimated plasma ejections in the solar atmosphere. They
are prevalent in active regions, the quiet Sun, and even coronal holes. They
display a range of temperatures, yet the nature of the cool components has not
been fully investigated. In this paper, we show the existence of the precursors
and quasi-periodic properties for two chromospheric jets, mainly utilizing the
He i 10830 {\AA} narrowband filtergrams taken by the Goode Solar Telescope
(GST). The extreme ultraviolet (EUV) counterparts present during the eruption
correspond to a blowout jet (jet 1) and a standard jet (jet 2), as observed by
the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamic Observatory
(SDO). The high-resolution He i 10830 {\AA} observation captures a long-lasting
precursor for jet 1, signified by a series of cool ejections. They are
recurrent jet-like features with a quasi-period of about five minutes. On the
other hand, the cool components of jet 2, recurrently accompanied by EUV
emissions, present a quasi-periodic behavior with a period of about five
minutes. Both the EUV brightening and He i 10830 {\AA} absorption show that
there was a precursor for jet 2 that occurred about five minutes before its
onset. We propose that the precursor of jet 1 may be the consequence of
chromospheric shock waves, since the five-minute oscillation from the
photosphere can leak into the chromosphere and develop into shocks. Then, we
find that the quasi-periodic behavior of the cool components of jet 2 may be
related to magnetic reconnections modulated by the oscillation in the
photosphere.
