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Very-high-energy (VHE) observations have revealed approximately 100 TeVsources in our Galaxy, and a significant fraction of them are underinvestigation for understanding their origin. We report our study of one ofthem, HESS~J1844$-$030. It is found possibly associated with the supernovaremnant (SNR) candidate G29.37+0.1, and detailed studies of the source regionat radio and X-ray frequencies have suggested that this SNR is a composite one,containing a pulsar wind nebula (PWN) powered by a candidate young pulsar. Asthe GeV source 4FGL~J1844.4$-$0306 is also located in the region with highpositional coincidence, we analyze its $\gamma$-ray data obtained with theLarge Area Telescope on-board the {\it Fermi Gamma-ray Space Telescope }. Wedetermine the GeV $\gamma$-ray emission is extended, described with aLog-Parabola function. The obtained spectrum can be connected to that of theVHE source HESS J1844$-$030. Given the properties and those frommulti-frequency studies, we discuss the origin of the $\gamma$-ray emission byconsidering that the two \gr\ sources are associated. Our modeling indicatesthat while the TeV part would have either a hadronic (from the SNR) or aleptonic origin (from the putative PWN), the GeV part would arise from ahadronic process. Thus we conclude that 4FGL~J1844.4$-$0306 is the likely GeVcounterpart to G29.37+0.1.

4FGL J1844.4-0306: high-energy emission likely from the supernova remnant G29.37+0.1