Magnetic adatoms on superconductors induce Yu-Shiba-Rusinov (YSR) states, which are key to the design of low-dimensional correlated systems and topological superconductivity. Competing magnetic interactions and superconducting pairing lead to a rich phase diagram. Using a scanning tunneling microscope (STM), we position Fe atoms on 2H-NbSe2 to build a dimer with an odd-parity ground state, i.e., a partially screened YSR channel with the hybridized states spanning the Fermi level. This ground state makes the dimer a promising precursor for a topological YSR chain. By adding one atom at a time, we track the formation of YSR bands. The lowest-energy band crosses the Fermi level, and we find strong site-dependent spectral variations especially at the chain's terminations. We attribute these features to quantum spin effects and ferromagnetic coupling influenced by the local chemical environment.