The Shimosaka school
According to the Kyūshū National Museum, the Shimosaka are a school based in the village of Shimosaka (下坂), in the Sakata district of Ōmi province, today’s Nagahama; after the battle of Sekigahara (1600) they were called in by the lords linked to Ōmi and spread throughout the country. The Fukui City History Museum relates that those swordsmiths moved to Echizen at the end of the Sengoku period and that, around 1605 (Keichō 10), with the building of Fukui castle by Yūki Hideyasu, the great Shimosaka school formed there, with Yasutsugu at its head, alongside the swordsmiths who had come from Mino. According to the Japanese Wikipedia, the house of Echizen Yasutsugu was the head of the school and swordsmith to the shogunate until the end of the Edo period, and passed the name down from generation to generation.
His name
The Yamada cutting list writes it 下阪継広 (Shimosaka Tsuguhiro), with 阪 (saka) instead of 坂 (saka), according to the Japanese and the English Wikipedia. His blades are signed 近江守藤原継廣 (Ōmi no Kami Fujiwara Tsuguhiro), with the old form 廣 (hiro) of the last character, and a katana bears on the other side of the tang 越前住下坂 (Echizen jū Shimosaka): “resident of Echizen, Shimosaka”. That the Tsuguhiro of the list and that of the signatures are the same swordsmith is likely, from the name and the school, but none of the sources consulted says so.
His dates
The only date on record is that of a wakizashi, the one in the photo on the home page, signed 近江守藤原継廣 (Ōmi no Kami Fujiwara Tsuguhiro) and dated in the fifth month of 1680 (Enpō 8). His years of birth and death, his master, his kinship with the Yasutsugu house and the year in which he received the title of Ōmi no Kami are not recorded in the sources consulted.
Who he is confused with
Tomita Kiyama’s ranking of shintō swordsmiths includes a Sekishū jū Tsuguhiro, of Iwami province, who is another swordsmith, according to the translation of the Japanese Sword Index; the same list includes another Shimosaka of Echizen, Shimosaka Tadatsugu.