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We report the first comprehensive census of the satellite dwarf galaxiesaround NGC~55 ($2.1$~Mpc) as a part of the DECam Local Volume Exploration DEEP(DELVE-DEEP) survey. NGC~55 is one of four isolated, Magellanic analogs in theLocal Volume around which DELVE-DEEP aims to identify faint dwarfs and othersubstructures. We employ two complementary detection methods: one targets fullyresolved dwarf galaxies by identifying them as stellar over-densities, whilethe other focuses on semi-resolved dwarf galaxies, detecting them throughshredded unresolved light components. As shown through extensive tests withinjected galaxies, our search is sensitive to candidates down to $M_V \lesssim-6.6$ and surface brightness $\mu \lesssim 28.5$ mag arcsec$^{-2}$, and $\sim80\%$ complete down to $M_V \lesssim -7.8$. We do not report any new confirmedsatellites beyond two previously known systems, ESO 294-010 and NGC~55-dw1. Weconstruct the satellite luminosity function of NGC~55 and find it to beconsistent with the predictions from cosmological simulations. As one of thefirst complete luminosity functions for a Magellanic analog, our resultsprovide a glimpse of the constraints on low-mass-host satellite populationsthat will be further explored by upcoming surveys, such as the Vera C. RubinObservatory's Legacy Survey of Space and Time.

DELVE-DEEP Survey: The Faint Satellite System of NGC 55