  The first LHAASO catalog presents six mysterious Ultra-High-Energy (UHE)
$\gamma$-ray sources -- 1LHAASO J0007$+$5659u, 1LHAASO J0206$+$4302u, 1LHAASO
J0212$+$4254u, 1LHAASO J0216$+$4237u, 1LHAASO J1740$+$0948u and 1LHAASO
J1959$+$1129u, which have emission only detected by LHAASO-KM2A (energy $>$ 25
TeV). No significant counterparts of these six sources are observed, except the
two pulsars PSR J0218$+$4232 and PSR J1740$+$1000. All the six sources are out
of Galactic plane with galactic latitudes (absolute value) over 5$^{\circ}$.
Three of them -- 1LHAASO J0206$+$4302u, 1LHAASO J0212$+$4254u and 1LHAASO
J0216$+$4237u are connected on the significance map and forming a dumbbell-like
structure. They are close in position and show a similar spectral shape,
suggesting a physical association among them. In this work, we first present a
multi-wavelength and multi-messenger study of these six sources based on the
Fermi-LAT, Swift-XRT, Planck and LAMBDA datasets as well as the data of
IceCube. The corresponding leptonic and hadronic modeling results are also
provided. To explain the interesting dumbbell-like structure, we established a
traveling Pulsar Wind Nebula (PWN) model. Our model has the ability to explain
both the morphology and spectrum of KM2A. However, both a high proper-motion
speed $>$ 1000 km s$^{-1}$ and a short distance $<$ 1 kpc are required in our
model, which contradict the parameters of the only known nearby pulsar - PSR
J0218+4232. For more detailed researches on this structure, we intend to
utilize XMM-Newton to acquire X-ray data with higher sensitivity.
