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 powerful tracers for investigating the cosmic origins of elements. This paper expands on a recent study by us, in which the element fluorine was studied in seven open clusters; here we add six open clusters and 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 were determined to better understand the interplay between F and s-process elements. Our goal is to analyze the trend of F abundances across the Galactic disk based on metallicity and age. By comparing observational data with Galactic chemical evolution models, the origin of F can be better understood. The spectra were obtained from the high-resolution near-infrared 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 ($ 2.28, and 2.33 mu m), three K-band Mg I lines ($ 2.10, 2.11, and 2.15 mu m), and two Ce II lines in the H band ($ 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 for 8 field stars. The F and Ce abundances were investigated as a function of metallicity, age, and galactocentric distance. We also compared our findings with different Galactic chemical evolution models. 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. This finding is consistent with and, with the large sample size, reinforces the conclusion of our previous study.