The 117th Regiment of Foot ("The Royal Mallows") is a fictional Irish regiment mentioned in the works of Arthur Conan Doyle.
By its title it appears to have been a Royal regiment, thus it probably had royal blue facings on their uniforms and a royal blue field for their Regimental Colours. From its high seniority number, it could possibly have been one of the Honourable East India Company's European regiments absorbed by the British Army.
By the term "Mallow" it refers either to the town of Mallow, County Cork (Gaelic >Magh Ealla, "Plain of the Swans") or to a flowering plant of the Mallow family. Therefore its regimental badge might either be a Swan or a stylized Mallow Plant (or both).
Taking the town of Mallow as its headquarters, it would be assumed to be raised in County Cork, part of the province of Munster, the recruiting ground of the real-life Royal Munster Fusiliers.
The North Cork Rifles, a real-life British Army Militia unit on the Irish establishment, were headquartered in Mallow. They were the 9th (Militia) Battalion of the 60th King's Royal Rifle Corps from 1881 to 1908 and thus used the same cap badge as the KRRC.