  Co-orbital objects, also known as trojans, are frequently found in
simulations of planetary system formation. In these configurations, a planet
shares its orbit with other massive bodies. It is still unclear why there have
not been any co-orbitals discovered thus far in exoplanetary systems or even
pairs of planets found in such a 1:1 mean motion resonance. Reconciling
observations and theory is an open subject in the field. The main objective of
the TROY project is to conduct an exhaustive search for exotrojans using
diverse observational techniques. In this work, we analyze the radial velocity
time series informed by transits, focusing the search around low-mass stars. We
employed the alpha-test method on confirmed planets searching for shifts
between spectral and photometric mid-transit times. This technique is sensitive
to mass imbalances within the planetary orbit, allowing us to identify
non-negligible co-orbital masses. Among the 95 transiting planets examined, we
find one robust exotrojan candidate with a significant 3-sigma detection.
Additionally, 25 exoplanets show compatibility with the presence of exotrojan
companions at a 1-sigma level, requiring further observations to better
constrain their presence. For two of those weak candidates, we find dimmings in
their light curves within the predicted Lagrangian region. We established upper
limits on the co-orbital masses for either the candidates and null detections.
Our analysis reveals that current high-resolution spectrographs effectively
rule out co-orbitals more massive than Saturn around low-mass stars. This work
points out to dozens of targets that have the potential to better constraint
their exotrojan upper mass limit with dedicated radial velocity observations.
We also explored the potential of observing the secondary eclipses of the
confirmed exoplanets to enhance the exotrojan search.
