We investigate the coherent pump–probe spectroscopy of a three-level Λ system, 6s1/2F = 3, 4→6p3/2F′ = 4, in the hyperfine manifold of D2 transition (852 nm) of cesium with particular reference to the sub-Doppler linewidth resonance arising from Aulter–Townes (AT) splitting and the possibility of using it for realizing a scheme for tunable atomic frequency offset locking (AFOL). We discuss here the theoretical framework for a Λ system interacting with a coherent pump and probe and use it to describe the process of modulation transfer in the AT and electromagnetically induced transparency regimes. We further employ an experimental scheme consisting of a strong pump and a pair of weak probes to resolve the sub-Doppler linewidth (~8 MHz) AT resonance and study its dependence on pump intensity and detuning. In order to explore the possibility of using such a sub-Doppler linewidth resonance for AFOL, we use its first derivative signal as a frequency discriminator to stabilize the probe laser. The frequency stability of the probe is characterized by means of error signal analysis. This study reveals that while the frequency stability of the AT locked laser is limited by the pump laser, the tuning range of the offset frequency lock can cover the entire Doppler profile and its immediate neighbourhood, thereby providing a simple and cost effective alternative to the external modulator. The study described in this paper contributes to the discussion on the subtle link between dressed state spectroscopy and AFOL, which is relevant for developing a master–slave-type laser system in the domain of coherent photon–atom interaction.