Hobbits are never mentioned in The Silmarillion, but they must have originated somewhere in the East. We can probably count them among the Secondborn and assume that they awoke with the rest of humanity in Hildorien at the first rising of the Sun.
Hobbits first enter the histories as a quiet fisher-folk dwelling on (or in) the banks of the River Anduin. That's how Smeagol and his cousin were able to find the One Ring. They began moving west after evil things started to darken the Greenwood and it became known as Mirkwood.
Arround T.A. 1300 Hobbits had started to settle in Bree. In the year 1601, the lands that would become the Shire were ceded by King Argeleb II to the Hobbits led by the brothers Marcho and Blanco.
Hobbits migrated from Bree in T. A. 1601, led by the brothers Marcho and Blanco. Argeleb II of Arthedain granted them the lands beyond the Baranduin (Brandywine) River.
Hobbits never made it to Beleriand, so they were not in those stories. I don't think Tolkien conceived the idea of Hobbits when he was writing his Legendarium.