We present a sub-threshold search for gravitational-wave inspirals from binary neutron stars using data from the first part of the fourth observing run of the LIGO-Virgo-KAGRA Collaboration. To enhance sensitivity to this targeted population, we incorporate a redshift-corrected population model based on radio observations of Galactic double neutron star systems. The search identifies a significant trigger with a false-alarm rate of about one per 50 years and a network signal-to-noise ratio of 9. 7, which was first reported by the LVK in low-latency processing as S231109ci and subsequently in the GWTC-4. 0 catalog as GW231109₂35456, a sub-threshold candidate. Accounting for a trials factor of five from the four LVK searches in GWTC-4. 0 and this new search, the false-alarm rate of the reported candidate is approximately one per 10 years. If this event is of astrophysical origin, the inferred source properties indicate component masses of 1. 40 to 2. 24 solar masses for the primary and 0. 97 to 1. 49 solar masses for the secondary, yielding a total mass of 2. 95 (+0. 38, -0. 07) solar masses. The event was localized to a region of 450 square degrees (90 percent probability) at a luminosity distance of 165 (+70, -69) megaparsecs.
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