From A Wiki of Ice and Fire
Rosby is the seat of House Rosby. It lies near King's Landing to the north. Rosby sits along the Rosby road, the shortest road between King's Landing and Duskendale. It is a small town, made up of daub-and-wattle huts lying around the castle of the Rosbys. Rosby's maester is Melwys.
A Clash of Kings
During the War of the Five Kings, the majority of the supply of food for King's Landing comes from Rosby and Stokeworth, both untouched by the war. Prince Tommen is held at Rosby on Tyrion Lannister's command to keep the royal family spread apart and make it harder for Stannis Baratheon to end the Lannister claim to the throne.
A Feast for Crows
Brienne of Tarth visits Rosby in her search for Sansa Stark. Lord Rosby's ward refuses to let Falyse Stokeworth and her husband, Ser Balman Byrch, stay the night when they travel to King's Landing.
A Dance with Dragons
The Rosby inheritance is brought up in a small council meeting. According to Grand Maester Pycelle, six claims have been put forward, but the council decides to settle the issue at a later date as they have more pressing matters to deal with.