  Context: The supernova remnant (SNR) G35.6-0.4 shows a non-thermal radio
shell, however, no {\gamma}-ray or X-ray counterparts have been found for it
thus far. One TeV source, HESS J1858+020, was found near the SNR and this
source is spatially associated with some clouds at 3.6 kpc. Aims: To attain a
better understanding of the origin of HESS J1858+020, we further investigate
the association between SNR cosmic rays (CRs) and the clouds through the
Fermi-LAT analysis and hadronic modeling. Methods: We performed the Fermi-LAT
analysis to explore the GeV emission in and around the SNR. We explored the SNR
physics with previously observed multi-wavelength data. We built a hadronic
model using runaway CRs of the SNR to explain the GeV-TeV observation. Results:
We found a hard GeV source (SrcX2) that is spatially coincident with both HESS
J1858+020 and a molecular cloud complex at 3.6 kpc. In addition, a soft GeV
source (SrcX1) was found at the northern edge of the SNR. The GeV spectrum of
SrcX2 connects well with the TeV spectrum of HESS J1858+020. The entire
{\gamma}-ray spectrum ranges from several GeV up to tens of TeV and it follows
a power-law with an index of ~2.15. We discuss several pieces of observational
evidence to support the middle-aged SNR argument. Using runaway CRs from the
SNR, our hadronic model explains the GeV-TeV emission at HESS J1858+020, with a
diffusion coefficient that is much lower than the Galactic value.
