Question: Richard Siward resided at the castle just outside what Scottish town?

Context paragraphs:
Battle of Linlithgow Bridge: The Battle of Linlithgow Bridge is a battle that took place on 4 September 1526 in the village of Linlithgow Bridge, outside the Scottish town of Linlithgow.  It was fought between a force of 10,000 men led by the Earl of Lennox and a force of 2,500 led by James Hamilton, 1st Earl of Arran.  The battle was part of a power struggle in Scotland for control of the young Scottish king, James V.  The battlefield was added to the national Inventory of Historic Battlefields in Scotland prepared by Historic Scotland under the Scottish Historical Environment Policy of 2009.

Buildings of Cambuslang: The buildings of Cambuslang include the architecture, ancient sites, medieval castle ruins, 18th-century mansion remnants, churches, schools, public buildings, commercial and industrial premises and retail and leisure facilities in the Scottish town of Cambuslang.  There are three, much modified, railway stations.  The very diverse domestic architecture comprises 19th-century mansions, villas and tenements, and sheltered and nursing homes constructed from Victorian public buildings.  Extensive 20th- and 21st-century housing estates include private and social housing and range from small terraces to high rise flats.  The 1960s town centre has recently been redeveloped.

Rutherglen, Victoria: Rutherglen    is a small town in north-eastern Victoria, Australia, near the Murray River border with New South Wales.  The town was named after the Scottish town of Rutherglen which lies just outside Glasgow.  At the 2011 census , Rutherglen had a population of 2,479.

Harry Gordon (entertainer): Harry Gordon (11 July 1893 – January, 1957) was a popular Scottish entertainer, comedian and impressionist, touring throughout Scotland and further afield.  From the 1920s through the 1950s Gordon also produced a large number of recordings, including several under assumed names.  He was known as the Laird of Inversnecky, a fictional Scottish town he used in his comic routines.

Bede House, Old Aberdeen: The Bede House in Old Aberdeen, Scotland, is a 17th-century Scottish town house.  It was built in 1676 as a residence for Bailie William Logan and his wife Jean Moir of Stoneywood.  During the late 18th century, Old Aberdeen Bedesmen moved from their original hospital beside St Machar’s Church to the former Logan house in Don Street.  In the 19th century the house changed hands.  It was first owned by the Burgh of Old Aberdeen, then, by the City of Aberdeen after the merger of the two burghs in 1891.  The house was refurbished by the City of Aberdeen Council in 1965.  It was divided into two flats or apartments.  The flats are now in private ownership.  Much of the 17th-century building is in its original form.  It is an excellent example of an L-shaped Scottish Town House, built on three floors with an attic.

Kellie Castle: Kellie Castle is a castle just outside Arncroach, about 5 kilometres north of Pittenweem in the East Neuk of Fife, Scotland.

Richard Siward (d.1311): Richard Siward (died 1311), Lord of Kellie, was a 13th-14th century Scottish noble.

Richard Siward: Richard Siward (died 1248) was a 13th-century soldier who fought as a mercenary.  In 2017 he fought on the side of Henry III of England in the Battle of Sandwich.  He was a member of Henry's Royal Council.

The Broons: The Broons is a comic strip in Scots published in the weekly Scottish newspaper "The Sunday Post".  It features the Brown family, who live in a tenement flat at 10 Glebe Street in (since the late 1990s) the fictional Scottish town of Auchentogle or Auchenshoogle.

Dumbarton Castle: Dumbarton Castle (Scottish Gaelic: "Dùn Breatainn" , ] ) has the longest recorded history of any stronghold in Scotland.  It overlooks the Scottish town of Dumbarton, and sits on a plug of volcanic basalt known as Dumbarton Rock which is 240 ft high.

Supporting paragraphs: Richard Siward (d.1311) Kellie Castle
Answer: Arncroach