  Open clusters are ideal tools for tracing the abundances of different
elements because their stars are expected to have the same age, distance, and
metallicity. Therefore, they serve as very powerful tracers for investigating
the cosmic origins of elements. This paper expands on a recent study by us,
where the element Fluorine was studied in seven previously open clusters,
adding six open clusters as well as eight field stars. The primary objective is
to determine the abundance of fluorine (F) to gain insight into its production
and evolution. The magnesium (Mg) abundances were derived to categorize the
field stars into high and low alpha disk populations. Additionally, cerium (Ce)
abundances are determined to better understand the interplay between F and
s-process elements. The spectra were obtained from the high-resolution
near-infra-red GIANO-B instrument at the Telescopio Nazionale Galileo (TNG).
For the derivation of the stellar parameters and abundances, the Python version
of Spectroscopy Made Easy (PySME) was used. OH, CN, and CO molecular lines and
band heads along with Fe I lines were used to determine the stellar parameters
in the H-band region. Two HF lines in the K-band ({\lambda}{\lambda} 2.28, 2.33
{\mu}m), three K-band Mg I lines ({\lambda}{\lambda} 2.10, 2.11, 2.15 {\mu}m),
and two Ce II lines in the H-band ({\lambda}{\lambda} 1.66, and 1.71 {\mu}m)
were used to derive the abundances of F, Mg, and Ce, respectively. F, Mg, and
Ce abundances were derived for 14 stars from 6 OCs, as well as 8 field stars.
The F and Ce abundances were investigated as a function of metallicity, age,
and Galactocentric distances. Our results indicate that asymptotic giant branch
stars and massive stars, including a subset of fast rotators (whose rotation
speed likely increases as metallicity decreases), are necessary to explain the
cosmic origin of F.
