  We present two evolved stars from the TAPAS (Tracking Advanced PlAnetary
Systems) with HARPS-N project devoted to RV precision measurements of
identified candidates within the PennState - Torun Centre for Astronomy Planet
Search. Evolved stars with planets are crucial to understand the dependency of
the planet formation mechanism on the mass and metallicity of the parent star
and to study star-planet interactions. The paper is based on precise radial
velocity (RV) measurements, for HD 103485 we collected 57 epochs over 3317 days
with the Hobby-Eberly Telescope and its High Resolution Spectrograph and 18
ultra-precise HARPS-N data over 919 days. For BD+03 2562 we collected 46 epochs
of HET data over 3380 days and 19 epochs of HARPS-N data over 919 days. We
present the analysis of the data and the search for correlations between the RV
signal and stellar activity, stellar rotation and photometric variability.
Based on the available data, we interpret the RV variations measured in both
stars as Keplerian motion. Both stars have masses close to Solar (1.11 and
1.14), very low metallicities ([Fe/H]=-0.50 and -0.71), and, both have Jupiter
planetary mass companions (m sin i=7 and 6.4 Mj), in close to terrestrial
orbits (1.4 and 1.3~au), with moderate eccentricities (e=0.34 and 0.2).
However, we cannot totally exclude that the signal in the case of HD~103485 is
due to rotational modulation of active regions. Based on the current data, we
conclude that BD+03 2562 has a bona fide planetary companion while for HD
103485 we cannot totally exclude that the best explanation for the RV signal
modulations is not the existence of a planet but stellar activity. If, the
interpretation remains that both stars have planetary companions they represent
systems orbiting very evolved stars with very low metallicities, a challenge to
the conditions required for the formation of massive giant gas planets.
