This paper presents a compact, linearly co-polarized in-band full-duplex (IBFD) antenna system for dual-band applications. The antenna system comprises two identical and closely spaced two-element arrays of quarter-wavelength shorted microstrip patch antennas (MPAs). A C-shaped slot is precisely etched near the shorted edge of each individual Microstrip Patch Antenna (MPA) to facilitate dual-band characteristics. At 2.4 GHz, the MPAs operate in the TM1/2,0 mode, with efficient radiation characteristics. At 3.5 GHz, these antennas switch to the TM1/2,2 mode, to maintain optimal performance and reliability in a second operational band. The |S11| ≤ -10 dB bandwidth for each MPA is 2.5 % at 2.4 GHz and 2 % at 3.5 GHz, with inter-port isolations exceeding 20 dB and 45 dB at 2.4 GHz and 3.5 GHz, respectively. Additionally, the antenna arrays achieve a broadside gain of 8.3 dBi at 2.4 GHz and 9.4 dBi at 3.5 GHz.