Evidence found of another siege
This one was at Edinburgh Castle in 1296, as the conclusion of Edward I’s campaign. In late April, his army was victorious at Dunbar, then James the Steward (Robert II’s grandfather) surrendered Roxburgh Castle. John Balliol fled north but was captured and deposed by July.
This article explains a little more about the siege, including the find of a stone projectile on the site, as a Virgin Hotel is proposed for part of Cowgate.